On the dynamics of isometries.
On the dynamics of polynomial-like mappings
On the dynamics of pseudo-Anosov homeomorphisms on representation varieties of surface groups.
On the dynamics of rational maps
On the dynamics of in a local field
Let be a local field, and where denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system are cycles and describe the cycles of this system.
On the entropy for group actions on the circle
We show that for a finitely generated group of C² circle diffeomorphisms, the entropy of the action equals the entropy of the restriction of the action to the non-wandering set.
On the entropy of Darboux functions
We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.
On the Entropy of the Geodesic Flow in Manifolds Without Conjugate Points.
On the envelope of a vector field
Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.
On the ergodic decomposition for a cocycle
Let (X,,μ,τ) be an ergodic dynamical system and φ be a measurable map from X to a locally compact second countable group G with left Haar measure . We consider the map defined on X × G by and the cocycle generated by φ. Using a characterization of the ergodic invariant measures for , we give the form of the ergodic decomposition of or more generally of the -invariant measures , where is χ∘φ-conformal for an exponential χ on G.
On the Ergodicity of Frame Flows.
On the ergodicity of many-dimensional focusing billiards
On the ergodicity of the Weyl sums cocycle
On the estimation of averages over infinite intervals with an application to average persistence in population models.
On the existence and non-existence of closed trajectories for some Hamiltonian flows.
On the existence and stability of unfoldings of equivariant two-parameter bifurcation problems.
On the existence of a periodic solution of a nonlinear ordinary differential equation.
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
On the existence of chaotic behaviour of diffeomorphisms
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.