Dr. Jorge Lewowicz

From Scholarpedia

Faculty of Engineering, University of the Republic, Montevideo Uruguay

Editor of:

Category:Topological Dynamics

Curator of:

Expansive systems

Author of:

Expansive systems

invitations

19 March 2008

Expansive systems

to author (agreed)

  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. Sensibility with respect to initial conditions. Invariance through conjugations. Perturbations.
2)Examples. Anosov and Quasi- Anosov. Hyperbolic Sets. Shifts. Denjois Map. Lewowicz Map.
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 .
4) Local connectedness of stable (unstable) sets on surfaces. Stable (Unstable) sets. Clasification of Expansive Systems on surfaces.
5) Results on clasification on higher dimension.
6)About the tangent map of Expansive Diffeomorphisms. Expansivity 

and Hiperbolicity. Resuls of Manie; other results.

7) Persistence and Topological Stability.
8) Concerning Continuous Expansive Systems.