Consider a Lagrangian of the form \[ L(x, \dot{x},q, \dot{q})=\frac{1}{2}(\dot{x}^2-x^2)+ \frac{1}{2}\dot{q}^2+(1+\delta (x))V(q) \] where $x$,$q \in \mathbb{R}$. Assuming that $\delta$ is bounded and $V$, periodic in $q$, is such that $V′(0)=0$, we prove existence of infinitely many solutions homoclinic to periodic orbits in the center manifold $q=0$, $\dot{q}=0$ of the corresponding system.
Existence of homoclinic solutions to periodic orbits in a center manifold
MACRI', MARTA
2004-01-01
Abstract
Consider a Lagrangian of the form \[ L(x, \dot{x},q, \dot{q})=\frac{1}{2}(\dot{x}^2-x^2)+ \frac{1}{2}\dot{q}^2+(1+\delta (x))V(q) \] where $x$,$q \in \mathbb{R}$. Assuming that $\delta$ is bounded and $V$, periodic in $q$, is such that $V′(0)=0$, we prove existence of infinitely many solutions homoclinic to periodic orbits in the center manifold $q=0$, $\dot{q}=0$ of the corresponding system.File in questo prodotto:
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