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5 papers · 1 filter
Galton-Watson processes in dynamical environments
Thomas Morand
We define a model of Galton Watson processes in dynamical environments where the environment evolves according to a dynamical system (X, T). Three behaviours are possible: uniforml…
Homeomorphism groups of basilica, rabbit and airplane Julia sets
Bruno Duchesne, Matteo Tarocchi
The airplane, the basilica and the Douady rabbit (and, more generally, rabbits with more than two ears) are well-known Julia sets of complex quadratic polynomials. In this paper we…
Non-convex Mather's theory and the Conley conjecture on the cotangent bundle of the torus
Claude Viterbo
The aim of this paper is to use the methods and results of symplectic homogenization (see [V4]) to prove existence of periodic orbits and invariant measures with rotation number de…
Sparsity of postcritically finite maps of and beyond: A complex analytic approach
Thomas Gauthier, Johan Taflin, Gabriel Vigny
An endomorphism of degree is said to be postcritically finite (or PCF) if its critical set is preperiodic, i.e. if there…
Numerical bounds on the regularity of an invariant function: Probability of extinction of Galton-Watson processes in dynamical environments
Thomas Morand
We study the Lyapunov exponents of models that are close to skew product systems over a C__ uniformly expanding transformation of the circle. For a continuous fibre map , analy…