-minimal subsets of the circle
Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.
self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
Let be a connected closed manifold and a self-map on . We say that is almost quasi-unipotent if every eigenvalue of the map (the induced map on the -th homology group of ) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of as eigenvalue of all the maps with odd is equal to the sum of the multiplicities of as eigenvalue of all the maps with even. We prove that if is having finitely many periodic points all of them hyperbolic,...
C¹ stability of endomorphisms on two-dimensional manifolds
A set of necessary conditions for C¹ stability of noninvertible maps is presented. It is proved that the conditions are sufficient for C¹ stability in compact oriented manifolds of dimension two. An example given by F. Przytycki in 1977 is shown to satisfy these conditions. It is the first example known of a C¹ stable map (noninvertible and nonexpanding) in a manifold of dimension two, while a wide class of examples are already known in every other dimension.
C¹ stable maps: examples without saddles
We give here the first examples of C¹ structurally stable maps on manifolds of dimension greater than two that are neither diffeomorphisms nor expanding. It is shown that an Axiom A endomorphism all of whose basic pieces are expanding or attracting is C¹ stable. A necessary condition for the existence of such examples is also given.
C¹-maps having hyperbolic periodic points
We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.
C¹-Stably Positively Expansive Maps
The notion of C¹-stably positively expansive differentiable maps on closed manifolds is introduced, and it is proved that a differentiable map f is C¹-stably positively expansive if and only if f is expanding. Furthermore, for such maps, the ε-time dependent stability is shown. As a result, every expanding map is ε-time dependent stable.
Canard cycles and homoclinic bifurcation in a 3 parameter family of vector fields on the plane.
Canonical realizations of Lie algebras associated with foliated coadjoint orbits
Center Manifolds are not C...
Central limit theorem for sampled sums of dependent random variables
We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, Stoch. Dynamics3 (2003) 477–497]. An application to parametric estimation by random sampling is also provided.
Centralisateurs des difféomorphismes de la demi-droite
Soit un difféomorphisme lisse de fixant seulement l’origine, et son centralisateur dans le groupe des difféomorphismes . Des résultat classiques de Kopell et Szekeres montrent que est toujours un groupe à un paramètre. En revanche, Sergeraert a construit un dont le centralisateur est réduit au groupe des itérés de . On présente ici le résultat principal de [3] : peut en fait être un sous-groupe propre et non-dénombrable (donc dense) de .
Certain closed flows on a 2-manifold
Chaos and shadowing around a homoclinic tube.
Chaos in some planar nonautonomous polynomial differential equation
We show that under some assumptions on the function f the system generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.
Chaos synchronization of a fractional nonautonomous system
In this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL) analogy we synchronize the same system. The numerical results demonstrate the effectiveness of the proposed methods.
Chaotic attractors of two-dimensional invertible maps.
Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity.
Classification of recurrent domains for some holomorphic maps.
Classification of riemannian flows with transverse similarity structures
Closed orbits of -extension of ergodic toral automorphisms.