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@math.ist.utl.pt

Position	Professor Catedrático
Education	Ph.D. in Applied Mathematics, 1985, Brown University
	M.Sc. in Applied Mathematics, 1983, Brown University
	Licenciado in Electr. Engineering, 1975, Instituto Superior Técnico
Research	Center for Mathematical Analysis, Geometry and Dynamical Systems, Director

Research Interests

Dynamical Systems, Differential Equations, Bifurcation Theory, Parabolic Partial Differential Equations

Selected Publications

• B. Fiedler, C. Rocha and M. Wolfrum,
  A Permutation Characterization of Sturm Global Attractors of Hamiltonian Type,
  J. Differential Equations, 252 no. 1 (2012), 588-623.
• W. Oliva and C. Rocha,
  Reducible Volterra and Levin-Nohel Retarded Equations with Infinite Delay,
  J. Dyn. Diff. Eq, 22 no. 3 (2010), 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 no. 2 (2010), 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 no. 1 (2008), 37-53.
• R. Czaja and C. Rocha,
  Transversality in Scalar Reaction-Diffusion Equations on a Circle,
  J. Differential Equations, 245 no. 3 (2008), 692-721.
• B. Fiedler and C. Rocha,
  Connectivity and Design of Planar Global Attractors of Sturm Type.  II: Connection Graphs,
  J. Differential Equations, 244 no.5 (2008), 1255-1286.
• C. Rocha,
  Realization of Period Maps of Planar Hamiltonian Systems,
  J. Dyn. Diff. Eq. 19 no. 3 (2007), 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 no.1 (2004), 99-138.
• P. Freitas and C. Rocha,
  Lyapunov Functionals and Stability for FitzHugh-Nagumo Systems,
  J. Differential Equations 169 no.1 (2001), 208-227.
• B. Fiedler and C. Rocha,
  Orbit Equivalence of Global Attractors of Semilinear Parabolic Differential Equations,
  Trans. Amer. Math. Soc. 352 no.1 (2000), 257-284.
• B. Fiedler and C. Rocha,
  Realization of Meander Permutations by Boundary Value Problems,
  J. Differential Equations 156 no.2 (1999), 282-308.
• B. Fiedler and C. Rocha,
  Heteroclinic Orbits of Semilinear Parabolic Equations,
  J. Differential Equations 125 no.1 (1996), 239-281.
• C. Rocha,
  Bifurcations in Discretized Reaction-Diffusion Equations,
  Resenhas IME-USP 4 no.1 (1994), 403-419.
• C. Rocha,
  On the Singular Problem for the Scalar Parabolic Equation with Variable Diffusion,
  J. of Math. Analysis Appl. 183 no.2 (1994), 413-428.
• C. Rocha,
  Properties of the Attractor of a Scalar Parabolic PDE,
  J. Dyn. Diff. Eq. 3 no.4 (1991), 575-591.
• G. Fusco and C. Rocha,
  A Permutation Related to the Dynamics of a Scalar Parabolic PDE,
  J. Differential Equations 91 no.1 (1991), 75-94.
• C. Rocha,
  Examples of Attractors in Scalar Reaction-Diffusion Equations,
  J. Differential Equations 73 no.1 (1988), 178-195.
• J. K. Hale and C. Rocha,
  Interaction of Diffusion and Boundary Conditions,
  Nonlinear Analysis 11 no.5 (1987), 633-649.
• J. K. Hale and C. Rocha,
  Varying Boundary Conditions with Large Diffusivity,
  J. Mathématiques Pures Appl. 66 no.2 (1987), 139-158.
• C. Rocha,
  Generic Properties of Equilibria of Reaction-Diffusion Equations,
  Proc. of the Roy. Soc. Edinburgh 101A no.1-2 (1985), 45-55.
• J. K. Hale and C. Rocha,
  Bifurcations in a Parabolic Equation with Variable Diffusion,
  Nonlinear Analysis 9 no.5 (1985), 479-494.

Proceedings

• 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.

Books (as editor)

• Differential Equations and Dynamical Systems,
  A. Galves, J. K. Hale and C. Rocha
  Fields Institute Communications 31, Amer. Math. Soc. 2002.
• International Conference on Differential Equations, Equadiff 95,
  L. Magalhães, C. Rocha and L. Sanchez
  World Scientific, Singapore 1993.

An Introduction to Infinite Dimensional Dynamical Systems

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