Related papers: All minimal Cantor systems are slow

Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…

We study the asymptotic behavior of solutions for $n$-component Ginzburg-Landau equations as $\ve \to 0$. We prove that the minimizers converges locally in any $C^k$-norm to a solution of a system of generalized harmonic map equations.

We prove existence of small amplitude, $2\pi \slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive…

Within the framework of tight binding models, aperiodic systems are mapped to a renormalized lattice with a dimer defect. In models exhibiting metal-insulator transition, the dimer acts like a resonant cavity and explains the existence of…

We prove the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. This result is…

We study minimal $\mathbb{Z}^d$-Cantor systems and the relationship between their speedups, their collections of invariant Borel measures, their associated unital dimension groups, and their orbit equivalence classes. In the particular case…

We answer a question by Judith Packer about the irreducibility of the wavelet representation associated to the Cantor set. We prove that if the QMF filter does not have constant absolute value, then the wavelet representations is reducible.

We characterize the complexity functions of subshifts up to asymptotic equivalence. The complexity function of every aperiodic function is non-decreasing, submultiplicative and grows at least linearly. We prove that conversely, every…

Given any pair of countable groups $G$ and $H$ with $G$ infinite, we construct a minimal, free, Cantor $G$-flow $X$ so that $H$ embeds into the group of automorphisms of $X$.

In this paper we study speedups of dynamical systems in the topological category. Specifically, we characterize when one minimal homeomorphism on a Cantor space is the speedup of another. We go on to provide a characterization for strong…

This paper is concerned with the asymptotic analysis of infinite systems of weakly coupled stationary Hamilton-Jacobi-Bellman equations as the discount factor tends to zero. With a specific Hamiltonian, we show the convergence of the…

We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under…

The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…

The purpose of this article is to extend the work by Anantharaman and Canc\`es [1], and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density…

We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity…

Under weaker regularity and compactness assumptions, we find the mountain-pass essential point, which is a novel extension of the classical Ambrosetti-Rabinowitz mountain pass theorem. We study the reversible superquadratic autonomous…

Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers and $\O$ be its integral ring. The convergent power series with coefficients in $\O$ are studied as dynamical systems on $\O$. A minimal decomposition theorem for…

This paper is devoted to the study of limit laws of entrance times to cylinder sets for Cantor minimal systems of zero entropy using their representation by means of ordered Bratteli diagrams. We study in detail substitution subshifts and…

We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…

We consider a group $G$ acting on a local dendrite $X$ (in particular on a graph). We give a full characterization of minimal sets of $G$ by showing that any minimal set $M$ of $G$ (whenever $X$ is different from a dendrite) is either a…