An example of infinitely many sinks for smooth interval maps.
An exotic flow on a compact surface
In 1988 Anosov [1] published the construction of an example of a flow (continuous real action) on a cylinder or annulus with a phase portrait strikingly different from our normal experience. It contains orbits whose -limit sets contain a non-periodic orbit along with a simple closed curve of fixed points, but these orbits do not wrap down on this simple closed curve in the usual way. In this paper we modify some of Anosov’s methods to construct a flow on a surface of genus with equally striking...
An extension of Markov partitions for a certain toral endomorphism.
Analysis of two step nilsequences
Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’s Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for two step nilsequences and give a classification scheme for them.
Analytic enclosure of the fundamental matrix solution
This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing...
Arithmetic on blocks.
Asymptotic stability of switching systems.
Asynchronous sliding block maps
Asynchronous sliding block maps
We define a notion of asynchronous sliding block map that can be realized by transducers labeled in A* × B*. We show that, under some conditions, it is possible to synchronize this transducer by state splitting, in order to get a transducer which defines the same sliding block map and which is labeled in A × Bk, where k is a constant integer. In the case of a transducer with a strongly connected graph, the synchronization process can be considered as an implementation of an algorithm of...
Attracteurs, orbites et ergodicité
Attracting dynamics of exponential maps.
Attractors and Inverse Limits.
This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.
Attractors with vanishing rotation number
Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a second fixed point. The main tools in the proof are Carath´eodory prime ends and fixed point index. The result is applicable to some concrete problems in the theory of periodic differential equations.
Automate des préfixes-suffixes associé à une substitution primitive
On explicite une conjugaison en mesure entre le décalage sur le système dynamique associé à une substitution primitive et une transformation adique sur le support d'un sous-shift de type fini, à savoir l'ensemble des chemins d'un automate dit des préfixes-suffixes. En caractérisant les préimages par la conjugaison des chemins périodiques de l'automate, on montre que cette conjugaison est injective sauf sur un ensemble dénombrable, sur lequel elle est finie-à-un. On en déduit l'existence d'une suite...
Automatic sequences generated by synchronizing automata fulfill the Sarnak conjecture
We prove that automatic sequences generated by synchronizing automata satisfy the full Sarnak conjecture. This is of particular interest, since Berlinkov proved recently that almost all automata are synchronizing.