TITLE

Homoclinic orbit to a center manifold

AUTHOR(S)
Bernard, Patrick
PUB. DATE
June 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Jun2003, Vol. 17 Issue 2, p121
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Studies a model system where the center manifold is a plane with harmonic oscillations on it. Lagrangian and Hamiltonian systems; Control at infinity; Systems with a hyperbolic fixed point; Convergence of sequences of periodic orbits; Existence of periodic orbits.
ACCESSION #
13604301

 

Related Articles

  • NON-KÄHLER SYMPLECTIC MANIFOLDS WITH TORIC SYMMETRIES. YI LIN; PELAYO, ALVARO // Quarterly Journal of Mathematics;Mar2011, Vol. 62 Issue 1, p103 

    Drawing on the classification of symplectic manifolds with coisotropic principal orbits by Duistermaat and Pelayo, in this note we exhibit families of compact symplectic manifolds, such that: (i) no two manifolds in a family are homotopically equivalent; (ii) each manifold in each family...

  • Contact Structure with Basic Potentials. Frescura, F.; Lubczonok, G. // International Journal of Theoretical Physics;Jan2005, Vol. 44 Issue 1, p35 

    This paper defines basic potentials for contact structure. Contact manifolds that admit a basic potential are shown to have an additional foliated structure of co-dimension 1. The properties of this new foliation, and its relation to the characteristic vector field, are explored.

  • Fibered Transverse Knots and the Bennequin Bound. Etnyre, John B.; Van Horn-Morris, Jeremy // IMRN: International Mathematics Research Notices;Apr2011, Vol. 2011 Issue 7, p1483 

    We prove that a nicely fibered link (by which we mean the binding of an open book) in a tight contact manifold (M, ?) with zero Giroux torsion has a transverse representative realizing the Bennequin bound if and only if the contact structure it supports (since it is also the binding of an open...

  • The structure of some classes of K-contact manifolds. Tripathi, Mukut Mani; Dwivedi, Mohit Kumar // Proceedings of the Indian Academy of Sciences: Mathematical Scie;Aug2008, Vol. 118 Issue 3, p371 

    We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ?-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a...

  • On Hamiltonian Systems with a Homoclinic Orbit to a Saddle-Center. Koltsova, O. // Journal of Mathematical Sciences;Jul2005, Vol. 128 Issue 2, p2787 

    We consider a real analytic Hamiltonian system with two degrees of freedom having a homoclinic orbit to a saddle-center equilibrium (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such a system and show that in the nonresonance case, there are...

  • ON THE CANONICAL EXTENSION OF A DIFFERENTIABLE MANIFOLD. Yildirim, Mehmet; Esin, Erdogan // Journal of Geometry;Nov2000, Vol. 69 Issue 1/2, p73 

    Studies the differential geometry of second canonical extension of a differentiable manifold. Vector fields; Geodesic submanifolds; Differential geometry of differentiable extensions.

  • The topology of quaternionic contact manifolds. Hladky, Robert // Annals of Global Analysis & Geometry;Jan2015, Vol. 47 Issue 1, p99 

    We explore the consequences of curvature and torsion on the topology of quaternionic contact manifolds with integrable vertical distribution establishing a general Myers theorem for quaternionic contact manifolds of positive horizontal Ricci curvature. We introduce the category of almost...

  • On the Pesin set of expansive geodesic flows in manifolds with no conjugate points. Ruggiero, O.; Rosas Meneses, Vladimir A. // Bulletin of the Brazilian Mathematical Society;Jul2003, Vol. 34 Issue 2, p263 

    In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.

  • Isoenergetic families of regular orbits on a given surface. Kotoulas, Thomas // Differential Geometry--Dynamical Systems;2008, p206 

    In the light of inverse problem of dynamics, we study homogeneous potentials of the form V (u, v)= umR( v/u ) of any degree m which produce a mono-parametric family of regular orbits f(u, v)=c on a certain surface. Especially, we are interested in isoenergetic orbits, i.e. orbits which are...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics