28 research outputs found

### Creation of blenders in the conservative setting

In this work we prove that each C^r conservative diffeomorphism with a pair
of hyperbolic periodic points of co-index one can be C^1-approximated by C^r
conservative diffeomorphisms having a blender.Comment: 4 figures, 16 figure

### Removing zero Lyapunov exponents in volume-preserving flows

Baraviera and Bonatti proved that it is possible to perturb, in the c^1
topology, a volume-preserving and partial hyperbolic diffeomorphism in order to
obtain a non-zero sum of all the Lyapunov exponents in the central direction.
In this article we obtain the analogous result for volume-preserving flows.Comment: 10 page

### Dominated Splitting and Pesin's Entropy Formula

Let $M$ be a compact manifold and $f:\,M\to M$ be a $C^1$ diffeomorphism on
$M$. If $\mu$ is an $f$-invariant probability measure which is absolutely
continuous relative to Lebesgue measure and for $\mu$ $a.\,\,e.\,\,x\in M,$
there is a dominated splitting $T_{orb(x)}M=E\oplus F$ on its orbit $orb(x)$,
then we give an estimation through Lyapunov characteristic exponents from below
in Pesin's entropy formula, i.e., the metric entropy $h_\mu(f)$ satisfies
$h_{\mu}(f)\geq\int \chi(x)d\mu,$ where
$\chi(x)=\sum_{i=1}^{dim\,F(x)}\lambda_i(x)$ and
$\lambda_1(x)\geq\lambda_2(x)\geq...\geq\lambda_{dim\,M}(x)$ are the Lyapunov
exponents at $x$ with respect to $\mu.$ Consequently, by using a dichotomy for
generic volume-preserving diffeomorphism we show that Pesin's entropy formula
holds for generic volume-preserving diffeomorphisms, which generalizes a result
of Tahzibi in dimension 2