Related papers: Fully chaotic conservative models for some torus h…

We show that a homeomorphism of a semi-locally connected compact metric space is equicontinuous if and only if the distance between the iterates of a given point and a given subcontinuum (not containing that point) is bounded away from…

We study the dynamics of generic volume-preserving automorphisms $f$ of a Stein manifold $X$ of dimension at least 2 with the volume density property. Among such $X$ are all connected linear algebraic groups (except $\mathbb{C}$ and…

We study topological properties of automorphisms of a 6-dimensional torus generated by integer matrices symplectic with respect to either the standard symplectic structure in six-dimensional linear space or a nonstandard symplectic…

A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a…

In this paper we investigate maps of the two-torus $\mathbb{T}^2$ of the form $T(x,y)=(x+\omega,g(x)+f(y))$ for Diophantine $\omega\in\mathbb{T}$ and for a class of maps $f,g:\mathbb{T}\to\mathbb{T}$, where each $g$ is strictly monotone and…

We discuss $C^0$-continuous homogeneous quasi-morphisms on the identity component of the group of compactly supported symplectomorphisms of a symplectic manifold. Such quasi-morphisms extend to the $C^0$-closure of this group inside the…

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…

Let $C(\mathbf I)$ be the set of all continuous self-maps from ${\mathbf I}=[0,1]$ with the topology of uniformly convergence. A map $f\in C({\mathbf I})$ is called a transitive map if for every pair of non-empty open sets $U,V$ in…

Below, by space we mean a separable metrizable zero-dimensional space. It is studied when the space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a…

Let S be a compact connected surface and let f be an element of the group Homeo\_0(S) of homeomorphisms of S isotopic to the identity. Denote by \tilde{f} a lift of f to the universal cover of S. Fix a fundamental domain D of this universal…

Let M be a smooth compact connected manifold, on which there exists an effective smooth circle action preserving a positive smooth volume. We show that on M, the smooth closure of the smooth volume-preserving conjugation class of some…

In this paper, we define a new notion of "freely tracing property by free chains" on $G$-like continua and we prove that a positive topological entropy homeomorphism on a $G$-like continuum admits a Cantor set $Z$ such that every tuple of…

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…

This paper surveys various results concerning stability for the dynamics of Lagrangian (or Hamiltonian) systems on compact manifolds. The main, positive results state, roughly, that if the configuration manifold carries a hyperbolic metric,…

We study the group of automorphisms of certain corona C*-algebras. As a corollary of a more general C*-algebraic result, we show that, under the Continuum Hypothesis, $\beta X\setminus X$ has nontrivial homeomorphisms, whenever $X$ is a…

We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an…

We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by applying round-off to planar rotations. All orbits of these maps are conjectured to be periodic. We let the angle of rotation approach pi/2, and…

We study the semi-discrete approximation of Aubry and Mather sets for Tonelli Lagrangians on the flat torus. Starting from the discrete Lax--Oleinik equation, we introduce natural discrete analogues of these sets and analyze their…

For any transitive piecewise monotonic map for which the set of periodic measures is dense in the set of ergodic invariant measures (such as monotonic mod one transformations and piecewise monotonic maps with two monotonic pieces), we show…

We show that a closed weakly-monotone symplectic manifold of dimension $2n$ which has minimal Chern number greater than or equal to $n+1$ and admits a Hamiltonian toric pseudo-rotation is necessarily monotone and its quantum homology is…