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José Pedro Gaivão graduated in Applied Mathematics from Universidade do Porto in 2005 with the final grade of 18 out of 20. On that same year he was awarded the Eng. António de Almeida prize for the highest classification in a Mathematics degree. In 2010 completed a PhD degree in Mathematics from the University of Warwick, under the supervision of Prof. Vassili Gelfreich, on the subject of exponentially small splitting of separatrices in Hamiltonian systems. From 2006 to 2010, J. P. Gaivão was an FCT PhD fellow and an FCT PostDoc fellow from 2010 to 2018. 2018, I joined ISEG - University of Lisbon as an Assistant Professor, and in April 2024, I was promoted to Associate Professor, further expanding my contributions to research and teaching. J. P. Gaivão joined ISEG - University of Lisbon as an Assistant Professor in 2018 and was promoted to Associate Professor in 2024. The area of expertise of J. P. Gaivão is Dynamical Systems and Ergodic Theory. He is particularly interested in understanding the general mechanisms of regular and chaotic dynamics in both conservative and dissipative systems. Since 2011, J. P. Gaivão has written and published numerous papers in peer-review international journals. All his papers report significant contributions to the knowledge of the field and have been published in peer-review international journals such as Advances in Mathematics, Communication in Mathematical Physics, Ergodic Theory & Dynamical Systems, Annales de l' Institut Fourier and Bulletin of the London Mathematical Society.
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Identification

Personal identification

Full name
José Pedro Gaivão

Citation names

  • Gaivão, José Pedro

Author identifiers

Ciência ID
6C12-F5B3-4E0F
ORCID iD
0000-0001-6368-1729

Telephones

Telephone
  • 213 925 87 (Professional)

Addresses

  • ISEG, Rua do Quelhas, 6, 1200-781, Lisboa, Lisboa, Portugal (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Portuguese (Mother tongue)
English Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
Italian Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1)
Education
Degree Classification
2006/09/01 - 2010/11/27
Concluded
 PhD in Mathematics (Doctor of Philosophy)
Major in Dynamical Systems
University of Warwick, United Kingdom
"EXPONENTIALLY SMALL SPLITTING OF INVARIANT MANIFOLDS NEAR A HAMILTONIAN-HOPT BIFURCATION" (THESIS/DISSERTATION)
2001/09/01 - 2005/09/01
Concluded
 Matemática Aplicada à Tecnologia (Licenciatura)
Universidade do Porto, Portugal
 18
Affiliation

Science

Category
Host institution 		Employer
2010/11/01 - 2018/04/02 Postdoc (Research) Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal

Teaching in Higher Education

Category
Host institution 		Employer
2024/04/05 - Current Associate Professor (University Teacher) ISEG Lisbon School of Economics and Management, Portugal
2018/02/01 - 2024/04/04 Assistant Professor (University Teacher) ISEG Lisbon School of Economics and Management, Portugal
2016 - 2019 Invited Assistant Professor (University Teacher) Universidade de Lisboa, Portugal
Projects

Contract

Designation Funders
2018/01/01 - Current New trends in Lyapunov Exponents
PTDC/MAT-PUR/29126/2017
Researcher
FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências, Portugal
 Associação para a Inovação e Desenvolvimento da FCT
Ongoing
2013/01/01 - 2015/03/31 Strategic Project - UI 491 - 2013-2014
PEst-OE/EGE/UI0491/2013
Researcher
Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
2011/01/01 - 2012/12/31 Strategic Project - UI 491 - 2011-2012
PEst-OE/EGE/UI0491/2011
Researcher
Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
2010/11/01 - 2012/10/01 Randomness in Deterministic Dynamical Systems and Applications
PTDC/MAT/105448/2008
Post-doc Fellow
Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
2006/10/01 - 2009/12/31 Sistemas Dinâmicos e Teoria do Controlo
SFRH/BD/30596/2006
PhD Student Fellow
University of Warwick, United Kingdom
 Fundação para a Ciência e a Tecnologia
Concluded
2006/01/01 - 2006/09/30 Sistemas de Controlo com Comutação: Contribuições Teóricas e Aplicações
SFRH/BD/25388/2005
PhD Student Fellow
Universidade do Porto Faculdade de Ciências, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Book chapter
  1. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, Diogo. "Polygonal Billiards with Strongly Contractive Reflection Laws: A Review of Some Hyperbolic Properties". In Difference Equations, Discrete Dynamical Systems and Applications, 179-190. Springer Berlin Heidelberg, 2016.
    10.1007/978-3-662-52927-0_14
Conference paper
  1. Del Magno, G.; Lopes Dias, J.; Duarte, P.; Gaivão, J.P.; Pinheiro, D.. "Polygonal billiards with strongly contractive reflection laws: A review of some hyperbolic properties". 2016.
    10.1007/978-3-662-52927-0_14
  2. Magalhães, H.; Lemos, J.M.; Mendonça, T.; Rocha, P.; Esteves, S.; Gaivão, J.. "Observer design in switching control of neuromuscular blockade: Clinical cases". 2006.
    10.1109/IEMBS.2006.259492
Edited book
  1. Lopes Dias, João; Duarte, Pedro; Gaivão, José Pedro; Klein, Silvius; Peixe, Telmo; Rocha, Jaqueline; Torres, Maria Joana. New Trends in Lyapunov Exponents. Springer International Publishing. 2023.
    10.1007/978-3-031-41316-2
Journal article
  1. Gaivão, José Pedro; Laurent, Michel; Nogueira, Arnaldo. "Rotation number of 2-interval piecewise affine maps". Aequationes mathematicae (2024): https://doi.org/10.1007/s00010-024-01064-2.
    10.1007/s00010-024-01064-2
  2. Bessa, Mário; Del Magno, Gianluigi; Lopes Dias, João; Gaivão, José Pedro; Torres, Maria Joana. "Billiards in generic convex bodies have positive topological entropy". Advances in Mathematics 442 (2024): 109592. https://doi.org/10.1016/j.aim.2024.109592.
    Published
  3. Gaivão, José Pedro; Nogueira, Arnaldo. "Dynamics of piecewise increasing contractions". Bulletin of the London Mathematical Society (2022):
    Accepted
  4. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Gaivão, José Pedro. "Hyperbolic Polygonal Billiards Close to 1-Dimensional Piecewise Expanding Maps". Journal of Statistical Physics 182 1 (2021): http://dx.doi.org/10.1007/s10955-020-02673-2.
    Published • 10.1007/s10955-020-02673-2
  5. Gaivão, José Pedro; Peixe, Telmo. "Periodic Attractor in the Discrete Time Best-Response Dynamics of the Rock-Paper-Scissors Game". Dynamic Games and Applications 11 3 (2020): 491-511. http://dx.doi.org/10.1007/s13235-020-00371-y.
    Published • 10.1007/s13235-020-00371-y
  6. Lopes Dias, João; Gaivão, José Pedro. "Linearization of Gevrey flows on Td with a Brjuno type arithmetical condition". Journal of Differential Equations 267 12 (2019): 7167-7212. http://dx.doi.org/10.1016/j.jde.2019.07.020.
    Published • 10.1016/j.jde.2019.07.020
  7. Magno, Gianluigi Del; Dias, João Lopes; Duarte, Pedro; Gaivão, José Pedro. "The attractor of piecewise expanding maps of the interval". Stochastics and Dynamics 20 02 (2019): 2050009. http://dx.doi.org/10.1142/s0219493720500094.
    Published • 10.1142/s0219493720500094
  8. Gaivão, José Pedro; Troubetzkoy, Serge. "lambda-stability of periodic billiard orbits". Nonlinearity 31 9 (2018): 4326-4353. http://dx.doi.org/10.1088/1361-6544/aacc47.
    Published • 10.1088/1361-6544/aacc47
  9. GAIVÃO, JOSÉ PEDRO. "Asymptotic periodicity in outer billiards with contraction". Ergodic Theory and Dynamical Systems 40 2 (2018): 402-417. http://dx.doi.org/10.1017/etds.2018.36.
    Published • 10.1017/etds.2018.36
  10. DEL MAGNO, GIANLUIGI; LOPES DIAS, JOÃO; DUARTE, PEDRO; GAIVÃO, JOSÉ PEDRO. "Hyperbolic polygonal billiards with finitely many ergodic SRB measures". Ergodic Theory and Dynamical Systems 38 6 (2017): 2062-2085. http://dx.doi.org/10.1017/etds.2016.119.
    Published • 10.1017/etds.2016.119
  11. Pedro Duarte; José Pedro Gaivão; Mohammad Soufi. "Hyperbolic billiards on polytopes with contracting reflection laws". Discrete and Continuous Dynamical Systems 37 6 (2017): 3079-3109. https://doi.org/10.3934%2Fdcds.2017132.
    Published • 10.3934/dcds.2017132
  12. Gianluigi Del Magno; Jose Pedro Gaivão; Eugene Gutkin. "Dissipative outer billiards: a case study". Dynamical Systems 30 1 (2014): 45-69. http://dx.doi.org/10.1080/14689367.2014.970130.
    Published • 10.1080/14689367.2014.970130
  13. Gianluigi Del Magno; João Lopes Dias; Pedro Duarte; José Pedro Gaivão. "Ergodicity of polygonal slap maps". Nonlinearity 27 8 (2014): 1969-1983. http://dx.doi.org/10.1088/0951-7715/27/8/1969.
    Published • 10.1088/0951-7715/27/8/1969
  14. Gianluigi Del Magno; João Lopes Dias; Pedro Duarte; José Pedro Gaivão; Diogo Pinheiro. "SRB Measures for Polygonal Billiards with Contracting Reflection Laws". Commun. Math. Phys. 329 2 (2014): 687-723. http://dx.doi.org/10.1007/s00220-014-1960-x.
    Published • 10.1007/s00220-014-1960-x
  15. Gaivão, José Pedro. "Analytic invariants for the 1:-1 resonance". Annales de l’institut Fourier 63 4 (2013): 1367-1426. http://dx.doi.org/10.5802/aif.2806.
    Published • 10.5802/aif.2806
  16. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Pedro Gaivão, José; Pinheiro, Diogo. "Chaos in the square billiard with a modified reflection law". Chaos: An Interdisciplinary Journal of Nonlinear Science 22 2 (2012): 026106. http://dx.doi.org/10.1063/1.3701992.
    Published • 10.1063/1.3701992
  17. Gaivão, José Pedro; Gelfreich, Vassili. "Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift–Hohenberg equation as an example". Nonlinearity 24 3 (2011): 677-698. http://dx.doi.org/10.1088/0951-7715/24/3/002.
    Published • 10.1088/0951-7715/24/3/002
Thesis / Dissertation
  1. "Exponentially small splitting of invariant manifolds near a Hamiltonian-Hopf bifurcation". PhD, University of Warwick, 2010. http://wrap.warwick.ac.uk/4534/.
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2019/09 Billiards inside strictly convex bodies with positive topological entropy Dynamics, Equations and Applications (DEA 2019)
AGH University of Science and Technology (Cracóvia, Poland)
2018/09 Survey of recent results in pinball billiards Dynamics Days Europe 2018
Loughborough University (Loughborough, United Kingdom)
2018/07 Periodic orbits in polygonal billiards Encontro Nacional da SPM
Instituto Politécnico de Bragança (Bragança, Portugal)
2017/07 Dynamics at weak resonances in area-preserving maps Llavefest: A broad perspective on finite and infinite dimensional Dynamical Systems
Universitat Barcelona (Barcelona, Spain)
2016/07 Conjugation of Gevrey torus flows Encontro Nacional da SPM
Instituto Politécnico de Setúbal (Setúbal, Portugal)
2016/07 Hyperbolic billiards on polytopes Encontro Nacional da SPM
Instituto Politécnico de Setúbal (Setúbal, Portugal)
2016/06 SRB measures for pinball polygonal billiards Warwick Dynamical Systems Workshop
University of Warwick (Coventry, United Kingdom)
2014/07 Contracting outer billiards Encontro Nacional da SPM
Universidade NOVA de Lisboa (Caparica, Portugal)
2014/02 Dissipative Polygonal Outer Billiards EURO Mini-conference on Optimization in the Natural Sciences
Universidade de Aveiro (Aveiro, Portugal)
2013/08 Splitting of separatrices near a Hamiltonian-Hopf bifurcation International Conference Planet Earth, Dynamics, Games and Science
Fundação Calouste Gulbenkian (Lisboa, Portugal)
2012/07 Splitting of separatrices near a Hamiltonian-Hopf bifurcation Encontro Nacional da SPM
Universidade do Algarve (Faro, Portugal)
2012/03 Chaos in the square billiard with a modified reflection law Conference Around scattering by obstacles and billiards
Universidade de Aveiro (Aveiro, Portugal)
2011/08 Splitting of separatrices near a Hamiltonian-Hopf bifurcation EQUADIFF 2011
Loughborough University (Loughborough, United Kingdom)
2006/09 Observer design in control of neuromuscular blockade 28th Annual International Conference IEEE in Medicine and Biology
Marriott Marquis Times Square (Nova Iorque, United States)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2019 - Current Stability of solutions of stochastic differential equations driven by the fractional Brownian motion
Co-supervisor
 Matemática Financeira (Master)
ISEG Lisbon School of Economics and Management, Portugal
2021 - 2021 Route optimization of the Bragança public transportation network
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2020 - 2020 Automatic balancing of production lines: bucket brigades
Supervisor
 Métodos Matemáticos para a Economia e Gestão de Empresas (Master)
ISEG Lisbon School of Economics and Management, Portugal
2019 - 2019 An application of machine learning for detecting money laundering and the financing of terrorism
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2019 - 2019 Pricing accounting services: a Portugal case study
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2018 - 2018 Periodic patterns in polling systems
Supervisor
 Matemática Financeira (Master)
ISEG Lisbon School of Economics and Management, Portugal
2018 - 2018 Analysis of healthcare suppliers
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2017 - 2017 Fictitious games: convergence to equilibria and chaotic play
Supervisor
 Matemática Financeira (Master)
ISEG Lisbon School of Economics and Management, Portugal
2017 - 2017 Backtesting às PDs e LGDs do Modelo de Imparidade
Supervisor
 Matemática Financeira (Master)
ISEG Lisbon School of Economics and Management, Portugal
2017 - 2017 Automatic reporting: a Dancake Portugal SA case study
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2017 - 2017 Enterprise Integration of SQL SERVER R SERVICES 2016
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2016 - 2016 Market analysis with clustering
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2016 - 2016 Departmental management dashboard
Supervisor
 Métodos Quantitativos para a Decisão Económica e Empresarial (Master)
ISEG Lisbon School of Economics and Management, Portugal
2015 - 2015 Hidden Markov Models for Credit Risk
Supervisor
 Matemática Financeira (Master)
ISEG Lisbon School of Economics and Management, Portugal
2015 - 2015 Market dynamics: study of an agent-based model
Supervisor
 Matemática Financeira (Master)
ISEG Lisbon School of Economics and Management, Portugal

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2022/11 - Current BOM Billiards https://sites.google.com/view/bombilliards/ (2022/11)
Seminar (Co-organisor)
2022/02/07 - 2022/02/11 LxDS workshop on New Trends in Lyapunov Exponents (2022/02/07 - 2022/02/11)
Workshop (Co-organisor)
 ISEG Lisbon School of Economics and Management, Portugal
2021/10/18 - 2021/10/22 LxDS mini-course on Determinantal Point Processes (2021/10/18 - 2021/10/22)
Other (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2021/07/19 - 2021/07/19 10th One Day Meeting on Dynamical Systems (2021/07/19 - 2021/07/19)
Seminar (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
2017/04/19 - 2021/03/24 CEMAPRE seminars (2017/04/19 - 2021/03/24)
Seminar (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
2020/07/07 - 2020/07/07 9th One Day Meeting on Dynamical Systems (2020/07/07 - 2020/07/07)
Seminar (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
2019/05/29 - 2019/05/31 LxDS Spring School 2019 (2019/05/29 - 2019/05/29)
Workshop (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2019/05/22 - 2019/05/22 8th One Day Meeting on Dynamical Systems (2019/05/22 - 2019/05/22)
Seminar (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2018/05/28 - 2018/05/30 LxDS Spring School 2018 (2018/05/28 - 2018/05/30)
Workshop (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
2016/03/04 - 2016/03/04 7th One Day Meeting on Dynamical Systems (2016/03/04 - 2016/03/04)
Seminar (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2015/01/19 - 2015/01/19 6th One Day Meeting on Dynamical Systems (2015/01/19 - 2015/01/19)
Seminar (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2014/02/10 - 2014/02/10 5th One Day Meeting on Dynamical Systems (2014/02/10 - 2014/02/10)
Seminar (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2013/08/28 - 2013/09/06 Thematic Session: Piecewise Smooth Dynamics International Conference Planet Earth, Dynamics, Games and Science (2013/08/28 - 2013/09/06)
Conference (Co-organisor)
 Fundação Calouste Gulbenkian, Portugal
2013/05/02 - 2013/05/02 4th One Day Meeting on Dynamical Systems (2013/05/02 - 2013/05/02)
Seminar (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
2013/02/04 - 2013/02/08 II Winter School on Stochastic Dynamics and Control (2013/02/04 - 2013/02/08)
Workshop (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
2012/12/12 - 2012/12/12 3rd One Day Meeting on Dynamical Systems (2012/12/12 - 2012/12/12)
Seminar (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
2012/01/16 - 2012/01/20 I Winter School on Stochastic Dynamics and Control (2012/01/16 - 2012/01/20)
Workshop (Co-organisor)
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal

Jury of academic degree

Topic
Role 		Candidate name (Type of degree)
Institution / Organization
2021/09/10 Dinâmica Genérica de Bilhares Ovais em Superfícies de Curvatura Constante
(Thesis) Main arguer
 Rafael da Costa Pereira (PhD)
Universidade Federal de Minas Gerais Departamento de Matemática, Brazil
2020/01/06 Entropy formulas for systems with singular sets
(Thesis) Arguer
 David Mesquita (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2017/03/31 Asymptotic behavior of compact skew-product semiflows on Hilbert spaces
(Thesis) Arguer
 Glória Ferreira (PhD)
Universidade do Porto Faculdade de Ciências, Portugal

Association member

Society Organization name Role
2010/11/01 - Current CEMAPRE Membro integrado

Committee member

Activity description
Role 		Institution / Organization
2019/12 - 2021/12 Member of the executive commission of the Department of Mathematics at ISEG.
Member
 ISEG Lisbon School of Economics and Management, Portugal
2015/04 - 2021/04 Member of the executive board of CEMAPRE
Member
 Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal

Other jury / evaluation

Activity description Institution / Organization
2021/10/28 - 2021/10/28 Competition FONDECYT Regular 2022 Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT), Chile. Comisión Nacional de Investigación Científica y Tecnológica Fondo Nacional de Desarrollo Científico y Tecnológico, Chile
Distinctions

Award

2005 Prize Eng. António de Almeida
Fundação Engenheiro António de Almeida, Portugal