Existence of Periodic Orbits for Singular-hyperbolic Sets
نویسندگان
چکیده
It is well known that on every compact 3-manifold there is a C flow displaying a singular-hyperbolic isolated set which has no periodic orbits [BDV], [M1]. By contrast, in this paper we prove that every singular-hyperbolic attracting set of a C flow on a compact 3manifold has a periodic orbit. 2000 Math. Subj. Class. Primary: 37D30; Secondary: 37D45.
منابع مشابه
Orbits homoclinic to resonances: the Hamiltonian case
In this paper we develop methods to show the existence of orbits homoclinic or heteroclinic to periodic orbits, hyperbolic fixed points or combinations of hyperbolic fixed points and/or periodic orbits in a class of two-degree-offreedom, integrable Hamiltonian systems subject to arbitrary Hamiltonian perturbations. Our methods differ from previous methods in that the invariant sets (periodic or...
متن کامل5 M ar 2 00 3 Transitivity and homoclinic classes for singular - hyperbolic systems
A singular hyperbolic set is a partially hyperbolic set with singularities (all hyper-bolic) and volume expanding central direction [MPP1]. We study connected, singular-hyperbolic, attracting sets with dense closed orbits and only one singularity. These sets are shown to be transitive for most C r flows in the Baire's second category sence. In general these sets are shown to be either transitiv...
متن کاملNonplanar second species periodic and chaotic trajectories for the circular restricted three-body problem
For the circular restricted three-body problem of celestial mechanics with small secondary mass, we prove the existence of uniformly hyperbolic invariant sets of non-planar periodic and chaotic almost collision orbits. Poincaré conjectured existence of periodic ones and gave them the name “second species solutions”. We obtain large subshifts of finite type containing solutions of this type.
متن کاملComputation of Homoclinic Solutions to Periodic Orbits in a Reduced Water-wave Problem
This paper concerns homoclinic solutions to periodic orbits in a fourth-order Hamiltonian system arising from a reduction of the classical water-wave problem in the presence of surface tension. These solutions correspond to travelling solitary waves which converge to non-decaying ripples at innnity. An analytical result of Amick and Toland, showing the existence of such homoclinic orbits to sma...
متن کاملSymmetric homoclinic tangles in reversible systems
We study the dynamics near transverse intersections of stable and unstable manifolds of sheets of symmetric periodic orbits in reversible systems. We prove that the dynamics near such homoclinic and heteroclinic intersections is not C1 structurally stable. This is in marked contrast to the dynamics near transverse intersections in both general and conservative systems, which can be C1 structura...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006