On the construction of a -counterexample to the Hamiltonian Seifert conjecture in .
On the definition of strange nonchaotic attractor
The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove that a whole...
On the dimensions of certain incommensurably constructed sets.
On the Distribution of Periodic Points for ß-Shifts.
On the Dynamic Behaviour of Chebyshev Polynomials.
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 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 Ergodicity of Frame Flows.
On the existence and non-existence of closed trajectories for some Hamiltonian flows.
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the forcing relation for surface homeomorphisms
On the global asymptotic stability problem and the Jacobian conjecture
On the group of real analytic diffeomorphisms
The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.
On the Hausdorff dimension of a family of self-similar sets with complicated overlaps
We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff dimension...
On the Hausdorff dimension of piecewise hyperbolic attractors
We study non-invertible piecewise hyperbolic maps in the plane. The Hausdorff dimension of the attractor is calculated in terms of the Lyapunov exponents, provided that the map satisfies a transversality condition. Explicit examples of maps for which this condition holds are given.
On the instability of ground states for a Davey-Stewartson system
On the location of poles of Ruelle's zeta function for Gauss map
On the Magnification of Cantor Sets and their Limit Models.
On the optimality of double-bracket flows.
On the Periodic Points of Topological Markov Chains.