Teorie dynamických systémů
The -complex Bruno function and the Yoccoz function: a numerical study of the Marmi-Moussa-Yoccoz conjecture.
The -problem and holomorphic dynamics.
The conjugacy map over a Sturmian word.
The Abramov-Rokhlin Entropy Addition Formula for Amenable Group Actions.
The absolute continuity of the invariant measure of random iterated function systems with overlaps
We consider iterated function systems on the interval with random perturbation. Let be uniformly distributed in [1-ε,1+ ε] and let be contractions with fixpoints . We consider the iterated function system , where each of the maps is chosen with probability . It is shown that the invariant density is in L² and its L² norm does not grow faster than 1/√ε as ε vanishes. The proof relies on defining a piecewise hyperbolic dynamical system on the cube with an SRB-measure whose projection is the...
The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
The action spectrum near positive definite invariant tori
We show that the Birkhoff normal form near a positive definite KAM torus is given by the function of Mather. This observation is due to Siburg [Si2], [Si1] in dimension 2. It clarifies the link between the Birkhoff invariants and the action spectrum near the torus. Our extension to high dimension is made possible by a simplification of the proof given in [Si2].
The algebraic Bethe Ansatz and vacuum vectors.
The Algebraic Integrability of Geodesic Flow on S0(4).
The algebro-geometric Toda hierarchy initial value problem for complex-valued initial data.
The approximate Euler method for Lévy driven stochastic differential equations
The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
The arithmetic of curves defined by iteration
We show how the size of the Galois groups of iterates of a quadratic polynomial f can be parametrized by certain rational points on the curves Cₙ: y² = fⁿ(x) and their quadratic twists (here fⁿ denotes the nth iterate of f). To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality theorem...
The Art and Science of Symmetric Design
The asymptotic behavior of invariant collective motion.
The asymptotics of the Perron-Frobenius operator of a class of interval maps preserving infinite measures
We determine the asymptotic behaviour of the iterates of the Perron-Frobenius operator for specific interval maps with an indifferent fixed point which gives rise to an infinite invariant measure.
The attractors of the common differential operator are determined by hyperbolic and lacunary functions.
The automorphism group of the random lattice is not amenable
We prove that the automorphism group of the random lattice is not amenable, and we identify the universal minimal flow for the automorphism group of the random distributive lattice.
The average length of a trajectory in a certain billiard in a flat two-torus.