Related papers: On ergodic and mixing properties of the triangle m…

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…

Ergodic systems, being indecomposable are important part of the study of dynamical systems but if a system is not ergodic, it is natural to ask the following question: Is it possible to split it into ergodic systems in such a way that the…

We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional $S_{BG}[p(x)]…

The theory of ergodic optimization for distance-expanding maps is extended to Gauss's continued fraction map. Since the set of invariant probability measures is not weak$^*$ closed, we establish a characterisation of the closure of this…

We study measure-theoretical aspects of torus piecewise isometries. Not much is known about this type of dynamical systems, except for the special case of one-dimensional interval exchange mappings. The last case is fundamentally different…

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…

We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of…

Using an efficient one and two qubit gate simulator, operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two dimensional lattice, which is periodically driven by a…

We study nonlinear dynamics of the Earth's tropical climate system. For that, we apply a recently developed technique for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. The method…

Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetric maps of…

There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…

A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for…

This work surveys the topological and statistical properties of real quadratic maps and investigates the complex quadratic maps under holomorphic and non-holomorphic singular perturbations.

Here we present an ergodic theorem which adapts a Theorem by J. Elton to the classical thermodynamical formalism and to ergodic transport. First, we discuss how Elton's theorem can be used to characterise Gibbs measures for expanding maps.…

We prove that, for a $C^2$ partially hyperbolic endomorphism of the 2-torus which is strongly transitive, given an ergodic $u$-Gibbs measure that has positive center Lyapunov exponent and has full support, then either the map is special…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

We study the robustness of 3D intrinsic topogical order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations…

If a map has k transitivity classes of vertices that are subject to the action of the automorphism group, it is said to be k-uniform. The classification of 1-uniform maps on the torus is known. In this article, we classify 2-uniform maps on…

Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…