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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Spectral rigidity and joint integrability for Anosov diffeomorphisms on tori
环形 阿诺索夫微分同胚 谱刚度 联合可积性
2023/4/14
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.
ON SIMULTANEOUS LINEARIZATION OF DIFFEOMORPHISMS OF THE SPHERE
DIFFEOMORPHISMS SIMULTANEOUS LINEARIZATION
2015/9/29
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...
Dense properties of the space of the circle diffeomorphisms with a Liouville rotation number
circle diffeomorphism rotation number Liouville number conjugacy invariant measure fast approximation by conjugation
2011/9/23
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...
Bernoulli equilibrium states for surface diffeomorphisms
Equilibrium measures Countable Markov partitions Bernoulli
2011/9/14
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...
Embedding smooth and formal diffeomorphisms through the Jordan-Chevalley decomposition
local diffeomorphism normal form embedding flow
2011/9/14
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...
On the regularity of the composition of diffeomorphisms
composition diffeomorphisms Analysis of PDEs
2011/8/24
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 $s > 1/2\dim M + 1$...
Minimal Diffeomorphisms cannot satisfy Generalized Dominated Splitting
Dominated splitting Minimal system Invariant and ergodic measure Recurrence
2011/7/28
Abstract: We introduce a new notion called generalized dominated splitting which is weaker than classical dominated splitting. We use this notion to generalize a result of Zhang\cite{Zh}: every diffeo...
Groups of formal diffeomorphisms in several complex variables and closed one-forms
Groups of formal diffeomorphisms several complex variables closed one-forms
2011/1/21
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...
Perturbations of C1-diffeomorphisms and dynamics of generic conservative diffeomorphisms of surface
C1-diffeomorphisms dynamics generic conservative diffeomorphisms of surface
2010/11/24
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...
Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
Essential hyperbolicity homoclinic bifurcations dichotomy phenomenon/mechanism for diffeomorphisms
2010/11/22
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...
A lower bound for topological entropy of generic non Anosov symplectic diffeomorphisms
topological entropy Anosov symplectic diffeomorphisms
2010/11/17
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 ...
Arithmetic properties of centralizers of diffeomorphisms of the half-line
Arithmetic properties centralizers diffeomorphisms
2010/11/22
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...
Multisummability of unfoldings of tangent to the identity diffeomorphisms
resonant diffeomorphism bifurcation theory asymptotic expansions Gevrey
2010/12/8
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...
The Entropy Conjecture for Diffeomorphisms away from Tangencies
Entropy conjecture principal symbolic extensions
2011/1/17
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...