Commuting expanding dynamics.
Complex one-frequency cocycles
We show that on a dense open set of analytic one-frequency complex valued cocycles in arbitrary dimension Oseledets filtration is either dominated or trivial. The underlying mechanism is different from that of the Bochi-Viana Theorem for continuous cocycles, which links non-domination with discontinuity of the Lyapunov exponent. Indeed, in our setting the Lyapunov exponents are shown to depend continuously on the cocycle, even if the initial irrational frequency is allowed to vary. On the other...
Complexity and Chaos Theory in Art
Comportement asymptotique des valeurs propres du laplacien sur un ouvert à bord fractal
Computation of the topological entropy in chaotic biophysical bursting models for excitable cells.
Conditions under which a Geodesic Flow is Anosov.
Conformally Anosov flows in contact metric geometry.
Connected components of the strata of the moduli spaces of quadratic differentials
In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...
Connections between Morse sets for delay-differential equations.
Connexions hétéroclines et généricité d'une infinité de puits et de sources
Constructing complete chaotic maps with reciprocal structures.
Constructing multi-branches complete chaotic maps that preserve specified invariant density.
Construction de flots de Smale en dimension 3
Construction of invariant sets for Anosov diffeomorphisms and hyperbolic attractors
Continuity of the Hausdorff dimension for invariant subsets of interval maps.
Continuum-wise expansive diffeomorphisms.
In this paper, we show that the C1 interior of the set of all continuum-wise expansive diffeomorphisms of a closed manifold coincides with the C1 interior of the set of all expansive diffeomorphisms. And the C1 interior of the set of all continuum-wise fully expansive diffeomorphisms on a surface is investigated. Furthermore, we have necessary and sufficient conditions for a diffeomorphism belonging to these open sets to be Anosov.
Contracting singular cycles
Contracting-on-Average Baker Maps
We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.
Control techniques for chaotic dynamical systems
Controlling chaos through growth rate adjustment.