Related papers: Ping-pong dynamics of hyperbolic-like actions with…

We prove that every acylindrically hyperbolic group that has no non-trivial finite normal subgroup satisfies a strong ping pong property, the $P_{naive}$ property: for any finite collection of elements $h_1, \dots, h_k$, there exists…

We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…

A hyperbolic group acts by homeomorphisms on its Gromov boundary. We use a dynamical coding of boundary points to show that such actions are topologically stable in the dynamical sense: any nearby action is semi-conjugate to (and an…

Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group…

A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…

We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models; depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first…

A hyperbolic group acts by homeomorphisms on its Gromov boundary. We show that if this boundary is a topological n-sphere the action is topologically stable in the dynamical sense: any nearby action is semi-conjugate to the standard…

We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…

A subgroup of $\mathrm{Homeo}_+(\mathbb{S}^1)$ is M\"obius-like if every element is conjugate to an element of $\mathrm{PSL}(2,\mathbb{R})$. In general, a M\"obius-like subgroup of $\mathrm{Homeo}_+(\mathbb{S}^1)$ is not necessarily…

We discuss actions of free groups on the circle with "ping-pong" dynamics; these are dynamics determined by a finite amount of combinatorial data, analogous to Schottky domains or Markov partitions. Using this, we show that the free group…

We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…

We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further…

We adapt the Ping-Pong Lemma, which historically was used to study free products of groups, to the setting of the homeomorphism group of the unit interval. As a consequence, we isolate a large class of generating sets for subgroups of…

We prove that if $\phi,\psi\in Out(F_N)$ are hyperbolic iwips (irreducible with irreducible powers) such that $<\phi,\psi>\le Out(F_N)$ is not virtually cyclic then some high powers of $\phi$ and $\psi$ generate a free subgroup of rank two,…

We exhibit an infinite family of discrete subgroups of ${Sp}_4(\mathbb R)$ which have a number of remarkable properties. Our results are established by showing that each group plays ping-pong on an appropriate set of cones. The groups arise…

Let $G$ be a group acting properly and essentially on an irreducible, non-Euclidean finite dimensional CAT(0) cube complex $X$ without fixed points at infinity. We show that for any finite collection of simultaneously inessential subgroups…

We isolate a tractable class of HNN-extensions of a free group, namely, multiple HNN-extensions by basis-conjugating embeddings. For this class, we construct a normal form and establish a practical version of the ping-pong lemma that…

We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the whole system,…

In hyperbolic dynamics, a well-known result is: every hyperbolic Lyapunov stable set, is attracting; it's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics. This question is still open, although some…

The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motion of a point particle in this configuration space with…