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Martin Sambarino

Publications and source records attributed to Martin Sambarino.

10 recordsLinked to original sources
arXiv2023

Non contractible periodic orbits for generic hamiltonian diffeomorphisms of surfaces

Let $S$ be a closed surface of genus $g\geq 1$, furnished with an area form $ω$. We show that there exists an open and dense set ${\mathcal O_r}$ of the space of Hamiltonian diffeomorphisms of class $C^r$, $1\leq r\leq\infty$, endowed with the $C^r$-topology, such that every $f\in \mathcal O_r$ possesses infinitely many non contractible periodic orbits. We obtain a positive answer to a question asked by Viktor Ginzburg and Başak Gürel. The proof is a consequence of recent previous works of the authors [LecSa].

math.DS↗
arXiv2016

Stable Ergodicity and Accessibility for certain Partially Hyperbolic Diffeomorphisms with Bidimensional Center Leaves

We consider classes of partially hyperbolic diffeomorphism $f:M\to M$ with splitting $TM=E^s\oplus E^c\oplus E^u$ and $\dim E^c=2$. These classes include for instance (perturbations of) the product of Anosov and conservative surface diffeomorphisms, skew products of surface diffeomorphisms over Anosov, partially hyperbolic symplectomorphisms on manifolds of dimension four with bidimensional center foliation whose center leaves are all compact. We prove that accessibility holds in these classes for $C^1$ open and $C^r$ dense subsets and moreover they are stably ergodic.

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arXiv2012

Examples of Minimal Diffeomorphisms on $t^{2}$ Semiconjugated to an Ergodic Translation

We prove that for every $ε>0$ there exists a minimal diffeomorphism $f:\T^{2}\rightarrow\T^{2}$ of class $C^{3-ε}$ and semiconjugate to an ergodic traslation, and have the following properties: zero entropy, sensitivity with respect to initial conditions and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Mañé's example of derived from Anosov diffeomorphism on $\T^3.$

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arXiv2011

Partial Hyperbolicity and Homoclinic Tangencies

We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

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arXiv2009

Codimension one generic homoclinic classes with interior

We study generic diffeomorphisms with a homoclinc class with non empty interior and in particular those admitting a codimension one dominated splitting. We prove that if in the finest dominated splitting the extreme subbundles are one dimensional then the diffeomorphism is partially hyperbolic and from this we deduce that the diffeomorphism is transitive.

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arXiv2009

Bowen measure for derived from Anosov diffeomorphims

In this work we give general conditions under which a $C^0$ perturbation of an expansive homeomorphim with specification property has an unique Bowen measure, that is, there is an ergodic probability measure which is the unique measure maximizing the topological entropy. We apply these conditions to show that several derived from Anosov diffeomorphims have a unique Bowen measure.

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arXiv2003

Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting

We study the Ruelle dynamical determinant of a real analytic diffeomorphism on a compact surface, assuming that the tangent space over the nonwandering set admits a dominated splitting. Combining previous work of Pujals and Sambarino with methods introduced by Rugh, we show that the determinant is either entire or holomorphic in a (possibly multiply) slit plane.

math.DS↗