# Dr. Jorge Lewowicz

Editor of ScholarpediaCurator Index: 1

## Curator and author

Short description of what I plan to cover:

1. Introduction to discrete expansive systems. Sensitivity with respect to initial conditions. Invariance through conjugations. Perturbations.
2. Examples: Anosov and quasi-Anosov. Hyperbolic sets. Shifts. Denjois maps. Lewowicz maps.
3. General properties. No expansivity only for the future. Non-existence of stable (unstable) points. Existence of connected stable (unstable) sets. Application: There are no expansive systems in $$S^1$$.
4. Local connectedness of stable (unstable) sets on surfaces. Stable (unstable) sets. Classification of expansive systems on surfaces.
5. Results on classification on higher dimension.
6. About the tangent map of expansive diffeomorphisms. Expansivity and Hyperbolicity. Results of Manie, and other results.
7. Persistence and topological stability.
8. Concerning continuous expansive systems.