Dr. Jorge Lewowicz

Faculty of Engineering, University of the Republic, Montevideo Uruguay

Curator and author

• Expansive systems
• (2008) Jorge Lewowicz, Marcelo Cerminara

I expect to finish this article at the end of September

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.