Dr. Jorge Lewowicz
Faculty of Engineering, University of the Republic, Montevideo Uruguay
I expect to finish this article at the end of September
Short description of what I plan to cover:
- Introduction to discrete expansive systems. Sensitivity with respect to initial conditions. Invariance through conjugations. Perturbations.
- Examples: Anosov and quasi-Anosov. Hyperbolic sets. Shifts. Denjois maps. Lewowicz maps.
- 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 \(S^1\).
- Local connectedness of stable (unstable) sets on surfaces. Stable (unstable) sets. Classification of expansive systems on surfaces.
- Results on classification on higher dimension.
- About the tangent map of expansive diffeomorphisms. Expansivity and Hyperbolicity. Results of Manie, and other results.
- Persistence and topological stability.
- Concerning continuous expansive systems.