Evolution maps and symmetry. (English) Zbl 1496.37027
Summary: We describe in detail how the symmetries of equivariance and reversibility induce corresponding properties for the stable and unstable invariant manifolds and for the stable and unstable foliations for any sufficiently small Lipschitz perturbation of a linear hyperbolic dynamics. This requires establishing first a faithful correspondence between the reversibility and equivariance properties of the original dynamics and corresponding properties for its evolution map.
MSC:
| 37D05 | Dynamical systems with hyperbolic orbits and sets |
| 37D10 | Invariant manifold theory for dynamical systems |
| 37C75 | Stability theory for smooth dynamical systems |
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