Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes

Details Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes

2008-04-10

arxiv.org/abs/0804.1796v1

Mathematics

Dynamical Systems

50 pages

Scientific paper

We prove that for a generic $C^1$-diffeomorphism existence of a homoclinic
class with periodic saddles of different indices (dimension of the unstable
bundle) implies existence an invariant ergodic non-hyperbolic (one of the
Lyapunov exponents is equal to zero) measure of $f$.

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