-continuity of the Fröbenius-Perron semigroup.
-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,...
weakly chaotic functions with zero topological entropy and non- flat critical points.
-algebras associated with presentations of subshifts.
-integrability test for discrete equations via multiple scale expansions.
-conjugacy of holomorphic flows near a singularity
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.
Calcul de la dynamique de transformations linéaires contractantes mod 1 et arbre de Farey
Calcul explicite des constantes de renormalisation pour des classes particulières de fonctions unimodales
Calogero-Moser spaces and an adelic -algebra
We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.
Can drag force suppress Fermi acceleration in a bouncer model?
Canard cycles and homoclinic bifurcation in a 3 parameter family of vector fields on the plane.
Canonical forms for -structures in pseudo-riemannian manifolds
Canonical lift and exit law of the fundamental diffusion associated with a kleinian group
Canonical realizations of Lie algebras associated with foliated coadjoint orbits
Cantor bouquets, explosions, and Knaster continua: dynamic of complex exponentials.
We describe some of the interesting dynamical and topological properties of the complex exponential family λez and its associated Julia sets.