Homoclinic orbits of positive definite Lagrangian systems

Homoclinic Orbits and Chaos in Discretized Perturbed NLS Systems: Part I. Homoclinic Orbits

The existence of homoclinic orbits, for a finite-difference discretized form of a damped and driven perturbation of the focusing nonlinear Schroedinger equation under even periodic boundary conditions, is established. More specifically, for external parameters on a codimension 1 submanifold, the existence of homoclinic orbits is established through an argument which combines Melnikov analysis w...

Random Homoclinic Orbits

We introduce random homoclinic points and orbits for random dynamical systems with hyperbolic stationary orbits and investigate their meaning for irregular behaviour in form of a stochastic version of the Birkhoo-Smale Theorem. In particular we show that transversal random homoclinic points cause a conjugacy of the random dynamical system in a part of the phase space to a random shift system.

Breathers and homoclinic orbits

s of Short Reports final: June 27, 2002 http://www.camtp.uni-mb.si/chaos/2002/ A method to enhance noise reduction for data generated from a known differential equation P. G. Vaidya, Savita Kallappa Angadi Mathematical Modelling Unit National Institute of Advanced Studies, Bangalore, India There are several papers which show the use of principle component analysis to reduce noise from a discret...

Connecting orbits of time dependent Lagrangian systems

We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather in [7]. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps. A very natural class of problems in dynamical systems is the existence of ...

Relative Periodic Orbits of Symmetric Lagrangian Systems