相关论文: $C^1$-generic dynamics: tame and wild behaviour
We present a characterization of finite permutation groups which contain a transitive dihedral subgroup.
We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable…
We show generic $C^\infty$ hyperbolic flows (Axiom A and no cycles, but not transitive Anosov) commute with no $C^\infty$-diffeomorphism other than a time-t map of the flow itself. Kinematic expansivity, a substantial weakening of…
We extend to the critical (intermediate) regularity several results concerning rigidity for centralizers and group actions on the interval.
We discuss some classical and recent results and open problems on the statistical behavior of ergodic sums above toral translations, and their applications to Diophantine approximations and to ergodic properties of systems related to…
Stable accessibility for partially hyperbolic diffeomorphisms is central to their ergodic theory, and we establish its \(C^1\)-density among 1. all, 2. volume-preserving, 3. symplectic, and 4. contact partially hyperbolic flows. As…
We construct a family of partially hyperbolic skew-product diffeomorphisms on $\mathbb{T}^3$ that are robustly transitive and admitting two physical measures with intermingled basins. In particularly, all these diffeomorphisms are not…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
We show stable ergodicity of a class of conservative diffeomorphisms which do not have any hyperbolic invariant subbundle. Moreover the uniqueness of SRB measures for non-conservative $C^1$ perturbations of such diffeomorphisms. This class…
We report on experimental studies on the collective behavior of a strongly interacting Fermi gas with tunable interactions and variable temperature. A scissors mode excitation in an elliptical trap is used to characterize the dynamics of…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
In this paper we introduce and study some stronger forms of transitivity like total transitivity, weakly mixing for maps on G-spaces. We obtain their relationship with the earlier defined notion of strongly mixing for maps on G-spaces. We…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of…
For r at least 3, p at least 2, we classify all actions of the groups Diff^r_c(R) and Diff^r_+(S1) by C^p -diffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
We prove that non-trivial homoclinic classes of $C^r$-generic flows are topologically mixing. This implies that given $\Lambda$ a non-trivial $C^1$-robustly transitive set of a vector field $X$, there is a $C^1$-perturbation $Y$ of $X$ such…
We prove that within the space of ergodic Lebesgue-preserving C1 expanding maps of the circle, unbounded distortion is C1-generic.
For diffeomorphisms or for non-singular flows, there are many results relating properties persistent under C1 perturbations and global structures for the dynamics ( such as hyperbolicity, partial hyperbolicity, dominated splitting).…
The transitivity degree of a group $G$ is the supremum of all integers $k$ such that $G$ admits a faithful $k$-transitive action. Few obstructions are known to impose an upper bound on the transitivity degree for infinite groups. The…