Related papers: On Non-contractible Periodic Orbits and Bounded De…
In [DKY], it was conjectured that there is a uniform bound $B$, depending only on the degree $d$, so that any pair of holomorphic maps $f, g :\mathbb{P}^1\to\mathbb{P}^1$ with degree $d$ will either share all of their preperiodic points or…
We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts,…
Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by…
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 this paper we study the dynamics of a family of diffeomorphisms in $\bR^2$ defined by $ F(x,y)=(g(x)+h(y),h(x)), $ where $ g(x) $ is a unimodal $C^2$-map which has the same dynamical properties as the logistic map $P(x)=\mu x(1-x)$, and…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
We show that S. Saito's fixed point formula serves as a powerful tool for counting the number of isolated periodic points of an area-preserving surface map admitting periodic curves. His notion of periodic curves of types I and II plays a…
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…
In this paper, we discuss the existence of fixed points for integral type contractions in uniform spaces endowed with both a graph and an $E$-distance. We also give two sufficient conditions under which the fixed point is unique. Our main…
We prove that a topological homeomorphism conjugating two generic 1-parameter unfoldings of 1-variable complex analytic resonant diffeomorphisms is holomorphic or anti-holomorphic by restriction to the unperturbed parameter. We provide…
The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in…
In this note, we construct examples of bounded smooth convex domains with no non-trivial analytic discs on the boundary which possess a holomorphic self-map without fixed points so that the iterates do not converge to a point (that is, the…
We investigate the existence of higher order exceptional points (EPs) in non-Hermitian systems, and show that $\mu$-fold EPs are stable in $\mu-1$ dimensions in the presence of anti-unitary symmetries that are local in parameter space, such…
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted…
Let (U \subset {\mathbb R}^3) be an open set and (f:U \to f(U) \subset {\mathbb R}^3) be a homeomorphism. Let (p \in U) be a fixed point. It is known that, if (\{p\}) is not an isolated invariant set, the sequence of the fixed point indices…
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…
Michael Handel has proved in [Ha] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that turned out to be an efficient tool in the study of the dynamics of surface homeomorphisms. The present article…
A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers…
In this paper, we study the dynamical uniform boundedness principle over a family of rational maps with certain nontrivial automorphisms. Specifically, we consider a family of rational maps of an arbitrary degree $d\ge 2$ whose automorphism…