Related papers: Topological Dynamics of Exponential Maps on their …
We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…
We study the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets. We establish a uniform upper bound on the number of iterations it takes for every orbit of a rational matrix to escape a compact…
We study the relation between escape rates and pressure in general dynamical systems with holes, where pressure is defined to be the difference between entropy and the sum of positive Lyapunov exponents. Central to the discussion is the…
In this work we present a theoretical and numerical study of the behaviour of the maximum Lyapunov exponent for a generic coupled-map-lattice in the weak-coupling regime. We explain the observed results by introducing a suitable…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We…
A study of rational maps of the real or complex projective plane of degree two or more, concentrating on those which map an elliptic curve onto itself, necessarily by an expanding map. We describe relatively simple examples with a rich…
The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared…
In this work we treat a famous topic in Ergodic Theory and Dynamical Systems: uniformly expanding maps. We relate regularity of expanding maps and conjugacies with Lyapunov exponents, metric and topological entropies for expanding maps of…
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…
The emphasis of this course is on pluripotential methods in complex dynamics in higher dimension. They are based on the compactness properties of plurisubharmonic functions and on the theory of positive closed currents. Applications of…
Given an ergodic measure with positive entropy and only positive Lyapunov exponents, its dynamical quantifiers can be approximated by means of quantifiers of some family of uniformly expanding repellers. Here non-uniformly expanding maps…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. We provide a polynomial-time algorithm to decide CPEP for…
We develop a general technique for realising full closed subsets of the complex plane as wandering sets of entire functions. Using this construction, we solve a number of open problems. (1) We construct a counterexample to Eremenko's…
We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…
We study the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains $U$ of meromorphic maps $f$ with a finite degree on $U$. We prove that if $f|_U$ is of hyperbolic or simply parabolic type, then almost…
We study topological entropy of exactly Devaney chaotic maps on totally regular continua, i.e. on (topologically) rectifiable curves. After introducing the so-called P-Lipschitz maps (where P is a finite invariant set) we give an upper…
We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image…
We analyze some properties of a class of multiexponential maps appearing naturally in the geometric analysis of Carnot groups. We will see that such maps can be useful in at least two interesting problems. First, in relation to the analysis…