Related papers: Homoclinic orbit expansion of arbitrary trajectori…
Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the property of generating copies of…
We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a…
The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a…
In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate.…
An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $\hbar$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however,…
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
We report on transcritical bifurcations of periodic orbits in non-integrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical…
Recovering trajectories of quantum systems whose classical counterparts display chaotic behavior has been a subject that has received a lot of interest over the last decade. However, most of these studies have focused on driven and…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a…
We study behaviour of trajectories near a type Z heteroclinic network which is a union of two cycles. Analytical and numerical studies indicate that attractiveness of this network can be associated with various kinds of dynamics in its…
The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system.…
The secular approximation for the evolution of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple-star systems. In this approximation the orbits may change shape and…
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit…