# American Institute of Mathematical Sciences

November  2007, 18(4): 677-699. doi: 10.3934/dcds.2007.18.677

## Reversibility and equivariance in center manifolds of nonautonomous dynamics

 1 Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa 2 Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa

Received  June 2006 Revised  January 2007 Published  May 2007

We consider reversible and equivariant dynamical systems in Banach spaces, either defined by maps or flows. We show that for a reversible (respectively, equivariant) system, the dynamics on any center manifold in a certain class of graphs (namely $C^1$ graphs with Lipschitz first derivative) is also reversible (respectively, equivariant). We consider the general case of center manifolds for a nonuniformly partially hyperbolic dynamics, corresponding to the existence of a nonuniform exponential trichotomy of the linear variational equation. We also consider the case of nonautonomous dynamics.
Citation: Luis Barreira, Claudia Valls. Reversibility and equivariance in center manifolds of nonautonomous dynamics. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 677-699. doi: 10.3934/dcds.2007.18.677
 [1] Andy Hammerlindl, Jana Rodriguez Hertz, Raúl Ures. Ergodicity and partial hyperbolicity on Seifert manifolds. Journal of Modern Dynamics, 2020, 16: 331-348. doi: 10.3934/jmd.2020012 [2] Knut Hüper, Irina Markina, Fátima Silva Leite. A Lagrangian approach to extremal curves on Stiefel manifolds. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020031 [3] Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 [4] Harrison Bray. Ergodicity of Bowen–Margulis measure for the Benoist 3-manifolds. Journal of Modern Dynamics, 2020, 16: 305-329. doi: 10.3934/jmd.2020011 [5] Weisong Dong, Chang Li. Second order estimates for complex Hessian equations on Hermitian manifolds. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020377 [6] Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 217-256. doi: 10.3934/dcds.2020217 [7] João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138 [8] Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020453 [9] Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020108 [10] Shengbing Deng, Tingxi Hu, Chun-Lei Tang. $N-$Laplacian problems with critical double exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 987-1003. doi: 10.3934/dcds.2020306 [11] Manil T. Mohan. Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with "fading memory". Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020105

2019 Impact Factor: 1.338