0000000000711104
AUTHOR
Jairo Bochi
showing 2 related works from this author
Perturbation of the Lyapunov spectra of periodic orbits
2012
We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.
A criterion for zero averages and full support of ergodic measures
2018
International audience; Consider a homeomorphism $f$ defined on a compact metric space $X$ and a continuous map $\phi\colon X \to \mathbb{R}$. We provide an abstract criterion, called control at any scale with a long sparse tail for a point $x\in X$ and the map $\phi$, which guarantees that any weak* limit measure $\mu$ of the Birkhoff average of Dirac measures $\frac1n\sum_0^{n-1}\delta(f^i(x))$ s such that $\mu$-almost every point $y$ has a dense orbit in $X$ and the Birkhoff average of $\phi$ along the orbit of $y$ is zero.As an illustration of the strength of this criterion, we prove that the diffeomorphisms with nonhyperbolic ergodic measures form a $C^1$-open and dense subset of the s…