Carlos
Rocha
Departamento
de Matemática
Instituto Superior Técnico
Av. Rovisco Pais, 1049-001 Lisboa Codex
phone:
(351) 218417102
fax:
(351) 218417035
phone:
(351) 218417102
email:
crocha@tecnico.ulisboa.pt
Position
|
Professor
Catedrático (Aposentado Dez 2020)
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|
|
Education
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Ph.D.
in Applied Mathematics,
1985, Brown University
|
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M.Sc.
in Applied Mathematics,
1983, Brown University
|
|
Licenciado
in Electr.
Engineering, 1975, Instituto Superior Técnico
|
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Research
|
Center
for Mathematical
Analysis, Geometry and Dynamical Systems
|
Research Interests
Dynamical
Systems, Differential
Equations, Bifurcation Theory,
Parabolic Partial Differential Equations
Selected Publications
- G. Fusco and C.
Rocha
On the structure of the
infinitesimal generators of scalar one-dimensional semigroups with discrete
Lyapunov functionals,
São Paulo J.
Math. Sci.,
To
appear.
- B.
Fiedler and C. Rocha
Design of Sturm global attractors 2:
time‑reversible Chafee–Infante lattices of 3‑nose meanders,
São Paulo J.
Math. Sci.,
To
appear.
- B.
Fiedler and C. Rocha
Design
of Sturm global attractors 1: Meanders with three noses,
and reversibility,
Chaos:
An Interdisciplinary Journal of Nonlinear Science, 33,
083127
(2023).
- C.
Rocha
and B.
Fiedler
Meanders,
zero numbers and the cell structure of Sturm global attractors,
J. Dynam. Differential
Equations,
To
appear.
- B.
Fiedler and C. Rocha
Boundary
orders and geometry of the signed Thom-Smale complex for Sturm global
attractors,
J. Dynam. Differential
Equations, 34
(2022), 4: 2787-2818.
- B.
Fiedler and C. Rocha,
Sturm 3-ball global attractors 2:
Design of Thom-Smale complexes,
J. Dynam. Differential
Equations, 31
(2019), 3: 1549-1590.
- B.
Fiedler and C. Rocha,
Sturm 3-ball global attractors 3:
Examples of Thom-Smale complexes,
Discrete
Contin. Dyn. Syst., 38 (2018), 7: 3479-3545.
- B.
Fiedler and C. Rocha,
Sturm 3-ball global attractors 1: Thom-Smale
complexes and meanders,
São Paulo J.
Math. Sci., 12 (2018),
1: 18-67.
- R.
Czaja, W. Oliva and C. Rocha,
On
a definition of
Morse-Smale evolution processes,
Discrete
Contin. Dyn. Syst., 37 (2017), 7: 3601-3623.
- J.
Pimentel and C.
Rocha,
A
permutation related to non-compact global attractors for slowly
non-dissipative
systems,
J.
Dyn. Diff. Eq. 28 (2016),
1: 1-28.
- J.
Pimentel and C.
Rocha,
Non-compact global attractors for scalar
reaction-diffusion equations,
São Paulo J.
Math. Sci., 9
(2015), 299-390.
- B.
Fiedler and C. Rocha,
Schoenflies
spheres as boundaries of bounded unstable manifolds in gradient Sturm
systems,
J.
Dyn. Diff. Eq. 27 (2015), 3-4:
597-626.
- B.
Fiedler and C.
Rocha,
Nonlinear Sturm global attractors: unstable
manifold
decompositions as CW-complexes,
Discrete Contin. Dyn Syst., 34
(2014), 12: 5099-5122.
- B.
Fiedler, C. Ragazzo and C.
Rocha,
An explicit Lyapunov function for
mirror-symmetric parabolic partial differential equations on the circle,
Russian Math. Surveys,
69
(2014), 3: 419-433.
- C.
Rocha,
Orbit
Equivalence of Global Attractors for S1-Equivariant
Parabolic Equations,
São Paulo J.
Math. Sci., 6 (2012), 2:
365-374.
- B.
Fiedler, C. Rocha and M.
Wolfrum,
Sturm
global attractors for S1-equivariant
parabolic
equations,
Netw. Heterog. Media., 7 (2012), 4:
617-659.
- B.
Fiedler, C. Rocha and M.
Wolfrum,
A
Permutation Characterization of Sturm Global
Attractors of Hamiltonian Type,
J. Differential Equations, 252 (2012), 1:
588-623.
- W.
Oliva and C. Rocha,
Reducible
Volterra and Levin-Nohel Retarded
Equations with Infinite Delay,
J.
Dyn. Diff. Eq, 22 (2010), 3: 509-532.
- B.
Fiedler and C. Rocha,
Connectivity
and Design of Planar Global Attractors of
Sturm Type. III:
Small and Platonic Examples,
J.
Dyn. Diff. Eq, 22 (2010), 2:
121-162.
- B.
Fiedler and C. Rocha,
Connectivity
and Design of Planar Global Attractors of
Sturm Type. I:
Bipolar Orientations and
Hamiltonian Paths,
J.
Reine Angew. Math, 635
(2009), 71-96.
- W.
Oliva and C. Rocha,
Reducible
Volterra Retarded Equations with
Infinite Delay,
São Paulo J.
Math. Sci., 2 (2008), 1:
37-53.
- R.
Czaja and C. Rocha,
Transversality
in Scalar Reaction-Diffusion
Equations
on a Circle,
J. Differential Equations, 245 (2008), 3:
692-721.
- B.
Fiedler and C. Rocha,
Connectivity
and Design of Planar Global
Attractors of
Sturm Type. II: Connection
Graphs,
J. Differential Equations, 244
(2008), 5: 1255-1286.
- C.
Rocha,
Realization of Period Maps of Planar Hamiltonian Systems,
J.
Dyn. Diff. Eq. 19 (2007), 3:
571-591.
- B.
Fiedler, C. Rocha and M.
Wolfrum,
Heteroclinic Orbits Between Rotating Waves of Semilinear Parabolic
Equations on the Circle,
J. Differential Equations 201 (2004), 1:
99-138.
- P.
Freitas
and C. Rocha,
Lyapunov Functionals and Stability for FitzHugh-Nagumo Systems,
J. Differential Equations 169 (2001), 1:
208-227.
- B.
Fiedler and C. Rocha,
Orbit Equivalence of Global Attractors of Semilinear Parabolic
Differential Equations,
Trans. Amer. Math. Soc. 352 (2000),
no. 1,
257-284.
- B.
Fiedler and C. Rocha,
Realization of Meander Permutations by Boundary Value Problems,
J. Differential Equations 156 (1999), 2:
282-308.
- B.
Fiedler and C. Rocha,
Heteroclinic Orbits of Semilinear Parabolic Equations,
J. Differential Equations 125 (1996), 1:
239-281.
- C.
Rocha,
Bifurcations in Discretized Reaction-Diffusion Equations,
Resenhas IME-USP 4 (1994), 1:
403-419.
- C.
Rocha,
On the Singular Problem for the Scalar Parabolic Equation with Variable
Diffusion,
J. of Math. Analysis Appl. 183 (1994), 2:
413-428.
- C.
Rocha,
Properties of the Attractor of a Scalar Parabolic PDE,
J. Dyn. Diff. Eq. 3 (1991), 4:
575-591.
- G.
Fusco and C. Rocha,
A Permutation Related to the Dynamics of a Scalar Parabolic PDE,
J. Differential Equations 91 (1991), 1:
75-94.
- C.
Rocha,
Examples of Attractors in Scalar Reaction-Diffusion Equations,
J. Differential Equations 73 (1988), 1:
178-195.
- J.
K. Hale and C. Rocha,
Interaction of Diffusion and Boundary Conditions,
Nonlinear Analysis 11 (1987), 5:
633-649.
- J.
K. Hale and C. Rocha,
Varying Boundary Conditions with Large Diffusivity,
J. Mathématiques
Pures Appl. 66 (1987), 2:
139-158.
- C.
Rocha,
Generic Properties of Equilibria of Reaction-Diffusion Equations,
Proc. of the Roy. Soc. Edinburgh 101A
(1985), 1-2: 45-55.
- J.
K. Hale and C. Rocha,
Bifurcations in a Parabolic Equation with Variable Diffusion,
Nonlinear Analysis 9 (1985), 5:
479-494.
- C.
Rocha
and B.
Fiedler
Sturm
global attractors of
Hamiltonian type for semilinear parabolic equations,
in Nonlinear Partial
Differential Equations, Dynamical Systems and Their Applications, M.
Tanigushi (ed.),
RIMS
Kôkyûroku 1881,
(2014) 139-158.
- C.
Rocha,
Transversality in Semilinear Parabolic Equations on the Circle,
in Proceedings of the
International Conference on
Differential Equations - Equadiff 2003,
F. Dumortier, H. Broer, J.
Mawhin, A. Vanderbauwhede and
S. V. Lunel (eds.)
World Scientific,
(2005) 672-677.
- B.
Fiedler, C. Rocha, D. Salazar
and J. Solà-Morales,
Dynamics of Piecewise-Autonomous Bistable Parabolic Equations,
in Differential Equations and
Dynamical Systems,
Galves, Hale and Rocha (eds.)
Fields Institute
Communications 31,
(2002) 151-163.
- C.
Rocha,
Some Remarks on the Singular Problem for the Scalar Parabolic Equation
with Variable Diffusion,
in International Conference on
Differential Equations,
Equadiff 91, Perelló,
Simó and
Solà-Morales (eds.)
World Scientific,
(1993) 832-837.
- P.
Freitas
and C. Rocha,
Bogdanov Singularity in the FitzHugh-Nagumo Equations,
in International Conference on
Differential Equations,
Equadiff 91, Perelló,
Simó and
Solà-Morales (eds.)
World Scientific,
(1993) 496-500.
- C.
Rocha,
Heteroclinic Connections in Parabolic Equations,
in Advanced Topics in the
Theory of Dynamical Systems,
Fusco, Iannelli and Salvadori (eds.)
Academic Press,
(1989) 205-211.
- C.
Rocha,
Examples of Attractors in Scalar Reaction-Diffusion Equations,
in Dynamics of Infinite
Dimensional Systems, Chow
and Hale (eds.)
Springer-Verlag,
(1987) 257-272.