Bifurcations in One Dimension. I. The Nonwandering Set.
Bifurcations in One Dimension. II. A Versal Model for Bifurcations.
Biholomorphic maps with linear parts having Jordan blocks: linearization and resonance type phenomena.
Billiard complexity in the hypercube
We consider the billiard map in the hypercube of . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that is the order of magnitude of the complexity.
Birational canonical transformations and classical solutions of the sixth Painlevé equation
Bistable traveling waves for monotone semiflows with applications
This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. In an abstract setting, we establish the existence of traveling waves for discrete and continuous-time monotone semiflows in homogeneous and periodic habitats. The results are then extended to monotone semiflows with weak compactness. We also apply the theory to four classes of evolution systems.
Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem
It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms ϕ and ψ is equal to the number of coincidence points of ϕ̂ and ψ̂ on the unitary dual, if the Reidemeister number is finite. An affirmative answer to the bitwisted Dehn conjugacy problem for almost polycyclic groups is obtained. Finally, we explain why the Reidemeister numbers are always infinite for injective endomorphisms of Baumslag-Solitar groups.
Bounded orbits of flows on homogeneous spaces.
Bounded solutions to a system of second order ODEs and the Whitney pendulum
We give an existence theorem for bounded solutions to a system of second order ODEs. Dynamical applications are considered.
Braiding of the attractor and the failure of iterative algorithms.
Breaking Cycles on Surfaces.
-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...