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In this talk, we address on the strong rigidity properties from joint integrability in the setting of Anosov diffeomorphisms on tori. More specifically, for an irreducible Anosov diffeomorphism with s...
Mostly contracting di eomorphisms are the simplest examples of robustly nonuniformly hyperbolic systems. This paper studies the mixing properties of mostly contracting di eomorphisms.
Let R1, R2 . . . Rm be rotations generating SOd+1, d ≥ 2, and f1, f2 . . . fm be their small smooth perturbations. We show that {fα} can be simultaneously linearized if and only if the assocated ran...
Abstract: Given any Liouville number $\alpha$, it is shown that various subspaces are $C^\infty$-dense in the space of the orientation preserving $C^\infty$ diffeomorphisms of the circle with rotation...
Abstract: Suppose f is a $C^{1+\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theor...
Abstract: In [Xiang Zhang, The embedding flows of $C^{\infty}$ hyperbolic diffeomorphisms, J. Differential Equations 250 (2011), no. 5, 2283-2298] Zhang proved that any local smooth hyperbolic diffeom...
Abstract: For $M$ being a closed manifold or the Euclidean space we present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s > 1/2\dim M + 1$...
We study groups of formal diffeomorphisms in several complex variables. For abelian,metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential...
In the first part of this text we give a survey of the properties satisfied by the C1-generic conservative diffeomorphisms of compact surfaces. The main result that we will discuss is that a C1-generi...
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...
We prove that a $C^1-$generic symplectic diffeomorphism is either Anosov or the topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of the periodic ...
Let f be a smooth diffeomorphism of the half-line fixing only the origin and Z^r_f its centralizer in the group of C^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z^1_f i...
We prove the multisummability of the infinitesimal generator of unfoldings of finite codimension tangent to the identity 1-dimensional local complex analytic diffeomorphisms. We also prove the multisu...
We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant.Consequently, such diffeomorphisms satisfy Shub’s entropy conjectu...
We prove that for every ǫ > 0 there exists a minimal diffeomorphism f : T2 ! T2 of class C3−ǫ and semiconjugate to an ergodic traslation, and have the following properties: zero entrop...

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