Related papers: Tame dynamics and robust transitivity
We study groups of C^1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly-orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that…
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we show that a broad class of real-analytic deformations of…
We consider diffeomorphisms $f$ with heterodimensional cycles of co-index two, associated with saddles $P$ and $Q$ having unstable indices $\ell$ and $\ell+2$, respectively. In a partially hyperbolic setting, where a two-dimensional center…
In this work, we investigate the dynamics of a general non-autonomous system generated by a commutative family of homeomorphisms. In particular, we investigate properties such as periodicity, equicontinuity, minimality and transitivity for…
Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We study the orbit behavior of a four dimensional smooth symplectic diffeomorphism $f$ near a homoclinic orbit $\Gamma$ to an 1-elliptic fixed point under some natural genericity assumptions. 1-elliptic fixed point has two real eigenvalues…
We construct diffeomorphisms in dimension $d\geq 2$ exhibiting $C^1$-robust heteroclinic tangencies.
The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can…
If $N \subset \R$ is a separable II$_1$-factor, the space $\Hom(N,\R)$ of unitary equivalence classes of unital *-homomorphisms $N \to \R$ is shown to have a surprisingly rich structure. If $N$ is not hyperfinite, $\Hom(N,\R)$ is an…
In this paper, we study the action on C^n of any group G of holomorphic diffeomorphisms (automorphisms) of C^n fixing 0. Suppose that there is x in C^n, having an orbit which generates C^n and also E(x)=C^n, where E(x) is the vector space…
In this paper, we study stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. Such actions are known to exist only on one-dimensional manifolds. The aim of this paper is to introduce a geometric method to…
We study diffeomorphisms $f$ with heterodimensional cycles, that is, heteroclinic cycles associated to saddles $p$ and $q$ with different indices. Such a cycle is called fragile if there is no diffeomorphism close to $f$ with a robust cycle…
We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in 2D that interact via repulsive contact forces. We measure the structural relaxation times obtained from the…
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…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Given a compact metric space $X$ and an upper semicontinuous function $F\colon X \to 2^X$, we explore the dynamic system $(X,F)$. In this study, we introduce new concepts, demonstrate various results, and provide numerous examples. In…
This paper generalizes the classical notion of turbulence from dynamical systems generated by continuous functions to those defined by closed relations on compact metric spaces. Using the Mahavier product and the associated shift map, we…
It is ``folklore'' that the solution to a set reachability problem for a dynamical system is only noncomputable because of non-robustness reasons. A robustness condition that can be imposed on a dynamical system is the requirement of the…