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Equadiff 2007
August 5-11, 2007
Vienna University of Technology
Vienna, Austria

Organizers
Anton Arnold, Josef Hofbauer, Christian Schmeiser, Alois Steindl, Peter Szmolyan, Gerald Teschl, Josef Teichmann

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Non-hyperbolic measures for non-hyperbolic homoclinic classes.
by
Lorenzo Diaz
PUC-Rio, Brazil

2. Lorenzo J. Diaz, PUC-Rio, Brazil

title:Non-hyperbolic measures for non-hyperbolic homoclinic classes.

abstract: We first discuss the relevance of homoclinic classes and review some recent topological properties of homoclinic classes containing points with different indices (dimension of the unstable bundle): as distribution of periodic points, supergrowth of the number of periodic points inside the class, and creation of heterodimensional cycles.

Finally, we prove that homoclinic classes of C1-generic diffeomorphisms containing saddles with different indices have non-hyperbolic ergodic measures whose support is uncountable. This is a joint work with Gorodetski.

Date received: July 6, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavl-13.