Related papers: Dynamics of annulus maps III: completeness

Let $f$ be a homeomorphism of the closed annulus $A$ that preserves orientation, boundary components and that has a lift $\tilde f$ to the infinite strip $\tilde A$ which is transitive. We show that, if the rotation number of both boundary…

Let M to B, N to B be fibrations and f1,f2 :M to N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f1,f2 over B to a coincidence free pair of maps.In…

The dynamical degree of a dominant rational map $f:\mathbb{P}^N\rightarrow\mathbb{P}^N$ is the quantity $\delta(f):=\lim(\text{deg} f^n)^{1/n}$. We study the variation of dynamical degrees in 1-parameter families of maps $f_T$. We make a…

We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…

We consider two classes of piecewise expanding maps $T$ of $[0,1]$: a class of uniformly expanding maps for which the Perron-Frobenius operator has a spectral gap in the space of bounded variation functions, and a class of expanding maps…

We prove a generalization of the Poincar\'e-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the…

We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if…

This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular…

Given two maps f1 and f2 from the sphere Sm to an n-manifold N, when are they loose, i.e. when can they be deformed away from one another? We study the geometry of their (generic) coincidence locus and its Nielsen decomposition. On the one…

We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if $A$ is completely invariant (i.e. $f^{-1}(A)=A$), and if $\mu$ is an arbitrary $f$-invariant…

We introduce an algebraicity criteria. It has the following form: under certain conditions, an analytic subvariety of some algebriac variety over a global field $K$, if it contains many $K$-points, then it is algebraic over $K.$ This gives…

An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…

Let $f$ be a $C^{1+\varepsilon}$ diffeomorphism of the closed annulus $A$ that preserves orientation and the boundary components, and $\widetilde{f}$ be a lift of $f$ to its universal covering space. Assume that $A$ is a Birkhoff region of…

We consider regular endomorphisms of the complex affine space with a degree gap $k$. They are endomorphisms $f$ of $\mathbb{A}_{\mathbb{C}}^{N}$ of the form…

In this article we consider homeomorphisms of the open annulus $\mathbb{A}=\mathbb{R}/\mathbb{Z}\times \mathbb{R}$ which are isotopic to the identity and preserve a Borel probability measure of full support, focusing on the existence of…

We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…

It is often the case that a covering map of the open annulus is semiconjugate to a map of the circle of the same degree. We investigate this possibility and its consequences on the dynamics. In particular, we address the problem of the…

Let F : P^n --> P^n be a morphism of degree d > 1 defined over C. The dynamical Mordell--Lang conjecture says that the intersection of an orbit O_F(P) and a subvariety X of P^n is usually finite. We consider the number of linear…

We present a one-parameter family of continuous, piecewise affine, area preserving maps of the square, which are inspired by a dynamical system in game theory. Interested in the coexistence of stochastic and (quasi-)periodic behaviour, we…

Let f : X --> X be a dominant rational map of a projective variety defined over a number field. An important geometric-dynamical invariant of f is its (first) dynamical degree d_f= lim SpecRadius((f^n)^*)^{1/n}. For algebraic points P of X…