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Identification

Personal identification

Full name
Carlos Rocha

Citation names

  • Rocha, Carlos

Author identifiers

Ciência ID
B312-F036-0E41
ORCID iD
0000-0002-3994-2834
Researcher Id
M-5058-2013
Scopus Author Id
7102396186
Education
Degree Classification
1985
Concluded
 Applied Mathematics (Doctor of Philosophy)
Brown University, United States
1981/09/01 - 1983/05/01
Concluded
 Applied Mathematics (Master)
Major in Mathematical Analysis, Differential Equations, Dynamical Systems.
Brown University, United States
1969/09/01 - 1975/09/01
Concluded
 Ciências de Engenharia - Engenharia Electrotécnica e de Computadores (Licenciatura)
Universidade de Lisboa Instituto Superior Técnico, Portugal
 17 valores
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
1995/03/16 - Current Full Professor (University Teacher) Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Projects

Grant

Designation Funders
2001/09/01 - 2008/08/30 Nonlinear analysis and dynamical systems
POCTI/MAT/199/2001
Principal investigator
Associação para o Desenvolvimento do Instituto Superior Técnico, Portugal
 Fundação para a Ciência e a Tecnologia
1997/09/01 - 2001/08/30 Nonlinear analysis and dynamical systems
POCTI/MAT/199/2001
Principal investigator
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
 Fundação para a Ciência e a Tecnologia
1993/09/01 - 1996/08/30 Methods of Nonlinear Analysis
STRDA/C/CEN/528/92
Principal investigator
Associação para o Desenvolvimento do Instituto Superior Técnico, Portugal
Concluded
1987/09/01 - 1991/08/30 Bifurcations in Attractors of Dissipative Systems
JNICT/87437
Principal investigator
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Concluded

Contract

Designation Funders
2020/01/01 - 2023/12/31 Center for Mathematical Analysis, Geometry and Dynamical Systems
UIDP/04459/2020
10.54499/UIDP/04459/2020
Principal investigator
Universidade de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2020/01/01 - 2023/12/31 Center for Mathematical Analysis, Geometry and Dynamical Systems
UIDB/04459/2020
10.54499/UIDB/04459/2020
Principal investigator
Universidade de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2019/01/01 - 2019/12/31 Center for Mathematical Analysis, Geometry and Dynamical Systems
UID/MAT/04459/2019
Principal investigator
Universidade de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2015/01/01 - 2018/12/31 Center for Mathematical Analysis, Geometry and Dynamical Systems
UID/MAT/04459/2013
Universidade de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2005/12/01 - 2007/11/30 Geometric Properties of Invariant Sets
PDCT/MAT/56476/2004
Principal investigator
Universidade de Lisboa Instituto Superior Técnico, Portugal

Universidade de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2004/09/01 - 2006/08/30 Internationalization of the Post-Doctoral Program in Mathematics.
Gulbenkian #20NMSL1032:
Principal investigator
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
 Fundação Calouste Gulbenkian
Concluded
Outputs

Publications

Journal article
  1. Bernold Fiedler; Carlos Rocha. "Design of Sturm global attractors 1: Meanders with three noses, and reversibility". Chaos: An Interdisciplinary Journal of Nonlinear Science (2023): https://doi.org/10.1063/5.0147634.
    10.1063/5.0147634
  2. Carlos Rocha; Bernold Fiedler. "Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors". J. Dynam. Differential Equations. (2022): https://link.springer.com/article/10.1007/s10884-020-09836-5.
    10.1007/s10884-020-09836-5
  3. Carlos Rocha; Bernold Fiedler. "Meanders, Zero Numbers and the Cell Structure of Sturm Global Attractors". Journal of Dynamics and Differential Equations (2021): https://doi.org/10.1007/s10884-021-10053-x.
    10.1007/s10884-021-10053-x
  4. Bernold Fiedler; Carlos Rocha. "Sturm 3-ball global attractors 1: Thom-Smale complexes and meanders". São Paulo Journal of Mathematical Sciences 12 1 (2018): 18-67. https://doi.org/10.1007/s40863-017-0082-8.
    10.1007/s40863-017-0082-8
  5. Bernold Fiedler; Carlos Rocha. "Sturm 3-Ball Global Attractors 2: Design of Thom–Smale Complexes". Journal of Dynamics and Differential Equations (2018): https://doi.org/10.1007/s10884-018-9665-z.
    10.1007/s10884-018-9665-z
  6. Rocha, Carlos. "On a definition of Morse-Smale evolution processes". Discrete Contin. Dyn. Syst. 37 7 (2017): 3601-3623. http://dx.doi.org/10.3934/dcds.2017155.
    10.3934/dcds.2017155
  7. Rocha, Carlos. "A permutation related to non-compact global attractors for slowly non-dissipative systems". J. Dynam. Differential Equations 28 1 (2016): 1-28. http://dx.doi.org/10.1007/s10884-014-9414-x.
    10.1007/s10884-014-9414-x
  8. Rocha, Carlos. "Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems". J. Dynam. Differential Equations 27 3-4 (2015): 597-626.
    10.1007/s10884-013-9311-8
  9. Rocha, Carlos. "Non-compact global attractors for scalar reaction-diffusion equations". S\~ao Paulo J. Math. Sci. 9 2 (2015): 299-310. http://dx.doi.org/10.1007/s40863-015-0022-4.
    10.1007/s40863-015-0022-4
  10. Fiedler, B.; Grotta-Ragazzo, C.; Rocha, C.. "An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle". Russian Mathematical Surveys 69 3 (2014): 419-433. http://www.scopus.com/inward/record.url?eid=2-s2.0-84906806513&partnerID=MN8TOARS.
    10.1070/RM2014v069n03ABEH004897
  11. Rocha, Carlos. "Nonlinear Sturm global attractors: Unstable manifold decompositions as regular CW-complexes". Discrete and Continuous Dynamical Systems 34 12 (2014): 5099-5122. http://www.scopus.com/inward/record.url?eid=2-s2.0-84902651390&partnerID=MN8TOARS.
    10.3934/dcds.2014.34.5099
  12. Fiedler, B.; Rocha, C.; Wolfrum, M.. "Sturm global attractors for S1-equivariant parabolic equations". Networks and Heterogeneous Media 7 4 (2012): 617-659. http://www.scopus.com/inward/record.url?eid=2-s2.0-84877333938&partnerID=MN8TOARS.
    10.3934/nhm.2012.7.617
  13. Fiedler, B.; Rocha, C.; Wolfrum, M.. "A permutation characterization of Sturm global attractors of Hamiltonian type". Journal of Differential Equations 252 1 (2012): 588-623. http://www.scopus.com/inward/record.url?eid=2-s2.0-80054123264&partnerID=MN8TOARS.
    10.1016/j.jde.2011.08.013
  14. Oliva, W.M.; Rocha, C.. "Reducible Volterra and Levin-Nohel Retarded Equations with Infinite Delay". Journal of Dynamics and Differential Equations 22 3 (2010): 509-532. http://www.scopus.com/inward/record.url?eid=2-s2.0-77956610692&partnerID=MN8TOARS.
    10.1007/s10884-010-9177-y
  15. Fiedler, B.; Rocha, C.. "Connectivity and design of planar global attractors of sturm type. III: Small and platonic examples". Journal of Dynamics and Differential Equations 22 2 (2010): 121-162. http://www.scopus.com/inward/record.url?eid=2-s2.0-77954313486&partnerID=MN8TOARS.
    10.1007/s10884-009-9149-2
  16. Fiedler, B.; Rocha, C.. "Connectivity and design of planar global attractors of Sturm type, I: Bipolar orientations and Hamiltonian paths". Journal fur die Reine und Angewandte Mathematik 635 (2009): 71-96. http://www.scopus.com/inward/record.url?eid=2-s2.0-71049174998&partnerID=MN8TOARS.
    10.1515/CRELLE.2009.076
  17. Czaja, R.; Rocha, C.. "Transversality in scalar reaction-diffusion equations on a circle". Journal of Differential Equations 245 3 (2008): 692-721. http://www.scopus.com/inward/record.url?eid=2-s2.0-44149110871&partnerID=MN8TOARS.
    10.1016/j.jde.2008.01.018
  18. Fiedler, B.; Rocha, C.. "Connectivity and design of planar global attractors of Sturm type. II: Connection graphs". Journal of Differential Equations 244 5 (2008): 1255-1286. http://www.scopus.com/inward/record.url?eid=2-s2.0-38549178403&partnerID=MN8TOARS.
    10.1016/j.jde.2007.09.015
  19. Oliva, Waldyr M.; Rocha, Carlos. "Reducible Volterra retarded equations with infinite delay". S\~ao Paulo J. Math. Sci. 2 1 (2008): 37-53.
  20. Rocha, C.. "Realization of period maps of planar hamiltonian systems". Journal of Dynamics and Differential Equations 19 3 (2007): 571-591. http://www.scopus.com/inward/record.url?eid=2-s2.0-35348945942&partnerID=MN8TOARS.
    10.1007/s10884-007-9081-2
  21. Rocha, C; Dumortier, F; Broer, H; Mawhin, J; Vanderbauwhede, A; Lunel, SV. "Transversality in semilinear parabolic equations on the circle". Equadiff 2003: International Conference on Differential Equations (2005): 672-677.
    10.1142/9789812702067_0112
  22. Fiedler, B.; Rocha, C.; Wolfrum, M.. "Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle". Journal of Differential Equations 201 1 (2004): 99-138. http://www.scopus.com/inward/record.url?eid=2-s2.0-2942668413&partnerID=MN8TOARS.
    10.1016/j.jde.2003.10.027
  23. Freitas, P.; Rocha, C.. "Lyapunov functionals and stability for FitzHugh-Nagumo systems". Journal of Differential Equations 169 1 (2001): 208-227. http://www.scopus.com/inward/record.url?eid=2-s2.0-0035216348&partnerID=MN8TOARS.
    10.1006/jdeq.2000.3901
  24. Fiedler, B.; Rocha, C.. "Orbit equivalence of global attractors of semilinear parabolic differential equations". Transactions of the American Mathematical Society 352 1 (2000): 257-284. http://www.scopus.com/inward/record.url?eid=2-s2.0-22844455201&partnerID=MN8TOARS.
  25. Fiedler, B.; Rocha, C.. "Realization of meander permutations by boundary value problems". Journal of Differential Equations 156 2 (1999): 282-308. http://www.scopus.com/inward/record.url?eid=2-s2.0-0033543056&partnerID=MN8TOARS.
  26. Fiedler, B.; Rocha, C.. "Heteroclinic orbits of semilinear parabolic equations". Journal of Differential Equations 125 1 (1996): 239-281. http://www.scopus.com/inward/record.url?eid=2-s2.0-0030577735&partnerID=MN8TOARS.
    10.1006/jdeq.1996.0031
  27. Rocha, Carlos. "Bifurcations in discretized reaction-diffusion equations - Dynamical phase transitions (S\tilde ao Paulo, 1994)". Resenhas 1 4 (1994): 403-419.
  28. Rocha, C.. "On the Singular Problem for the Scalar Parabolic Equation with Variable Diffusion". Journal of Mathematical Analysis and Applications 183 2 (1994): 413-428. http://www.scopus.com/inward/record.url?eid=2-s2.0-33746156085&partnerID=MN8TOARS.
    10.1006/jmaa.1994.1151
  29. Fusco, G.; Rocha, C.. "A permutation related to the dynamics of a scalar parabolic PDE". Journal of Differential Equations 91 1 (1991): 111-137. http://www.scopus.com/inward/record.url?eid=2-s2.0-0002238002&partnerID=MN8TOARS.
    10.1016/0022-0396(91)90134-U
  30. Rocha, C.. "Properties of the attractor of a scalar parabolic PDE". Journal of Dynamics and Differential Equations 3 4 (1991): 575-591. http://www.scopus.com/inward/record.url?eid=2-s2.0-0001032545&partnerID=MN8TOARS.
    10.1007/BF01049100
  31. Rocha, C.. "Examples of attractors in scalar reaction-diffusion equations". Journal of Differential Equations 73 1 (1988): 178-195. http://www.scopus.com/inward/record.url?eid=2-s2.0-38249027159&partnerID=MN8TOARS.
    10.1016/0022-0396(88)90124-6
  32. Hale, J.K.; Rocha, C.. "Interaction of diffusion and boundary conditions". Nonlinear Analysis 11 5 (1987): 633-649. http://www.scopus.com/inward/record.url?eid=2-s2.0-34047207185&partnerID=MN8TOARS.
    10.1016/0362-546X(87)90078-2
  33. HALE, JK; ROCHA, C. "VARYING BOUNDARY-CONDITIONS WITH LARGE DIFFUSIVITY". Journal De Mathematiques Pures Et Appliquees 66 2 (1987): 139-158.
  34. Hale, J.K.; Rocha, C.. "Bifurcations in a parabolic equation with variable diffusion". Nonlinear Analysis 9 5 (1985): 479-494. http://www.scopus.com/inward/record.url?eid=2-s2.0-0000413519&partnerID=MN8TOARS.
    10.1016/0362-546X(85)90007-0
  35. ROCHA, C. "GENERIC PROPERTIES OF EQUILIBRIA OF REACTION-DIFFUSION EQUATIONS WITH VARIABLE DIFFUSION". Proceedings of the Royal Society of Edinburgh Section a-Mathematics 101 (1985): 45-55.
Activities

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2011/09/01 - 2014/05/31 Asymptotic behavior of slowly non-dissipative systems
Supervisor
 Dynamical systems and differential equations (PhD)
Universidade de Lisboa Instituto Superior Técnico, Portugal
1993/09/01 - 1994/08/30 The method of two scales
Supervisor
 Dynamical systems and differential equations (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
1989/09/01 - 1990/08/30 Bogdanov singularity in the FitzHugh-Nagumo equations
Supervisor
 Dynamical systems and differential equations
Universidade de Lisboa Instituto Superior Técnico, Portugal

Mentoring / Tutoring

Topic Student name
2019/09/01 - 2020/08/30 Dynamical systems and differential equations Phillipo Lappicy
2005/09/01 - 2007/08/30 Dynamical systems and differential equations Radoslaw Martin Czaja
1995/09/01 - 1996/08/30 Dynamical systems and differential equations Joana Ventura
1989/09/01 - 1992/08/30 Dynamical systems and differential equations Rui Saramago
1990/09/01 - 1991/08/30 Dynamical systems and differential equations Luis Barreira