Homoclinic orbits for flows in R3
نویسنده
چکیده
2014 We propose a rough classification for volume contracting flows in R3 with chaotic behaviour. In the simplest cases, one looks at the nature of a homoclinic loop for the flow. Most configurations have been studied at length in the literature; here we examine briefly the « forgotten » case. J. Physique 45 (1984) 837-841 MAI 1984, 1
منابع مشابه
Attractors and Orbit-flip Homoclinic Orbits for Star Flows
We study star flows on closed 3-manifolds and prove that they either have a finite number of attractors or can be C1 approximated by vector fields with orbit-flip homoclinic orbits.
متن کاملMultiple Homoclinic Orbits in Conservative and Reversible Systems
I will consider dynamics near multiple homoclinic orbits to saddles in conservative and reversible flows. Suppose the system has two homoclinic orbits in the bellows configuration, where the homoclinic orbits approach the equilibrium along the same direction for positive and negative times. In conservative systems one finds one parameter families of suspended horseshoes, parameterized by the le...
متن کاملResonant Gluing bifurcations
We consider the codimension-three phenomenon of homoclinic bifurcations of flows containing a pair of orbits homoclinic to a saddle point whose principal eigenvalues are in resonance. We concentrate upon the simplest possible configuration, the so-called “figure-of-eight,” and reduce the dynamics near the homoclinic connections to those on a two-dimensional locally invariant centre manifold. Th...
متن کاملLimited to Ergodic Bil l iards
Abs t rac t , Sufficient conditions are found so that a family of smooth Hamiltonian flows limits to a billiard flow as a parameter e --~ 0. This limit is proved to be C 1 near non-singular orbits and C o near orbits tangent to the billiard boundary. These results are used to prove that scattering (thus ergodic) billiards with tangent periodic orbits or tangent homoclinic orbits produce nearby ...
متن کاملChaos in PDEs and Lax Pairs of Euler Equations
Recently, the author and collaborators have developed a systematic program for proving the existence of homoclinic orbits in partial differential equations. Two typical forms of homoclinic orbits thus obtained are: (1) transversal homoclinic orbits, (2) Silnikov homoclinic orbits. Around the transversal homoclinic orbits in infinite-dimensional autonomous systems, the author was able to prove t...
متن کامل