Abstract We consider analytic families of planar vector fields depending analytically on the parameters in Λ \Lambda that guarantee existence a (may be degenerate and with characteristic directions) monodromic singularity. characterize structure asymptotic Dulac series Poincaré map associated to si...

In the present paper, we study the Poincaré map associated to a periodic perturbation, both in space and time, of a linear Hamiltonian system. The dynamical system embodies the essential physics of stellar pulsations and provides a global and qualitative explanation of the chaotic oscillations observed in some stars. We show that this map is an area preserving one with an oscillating rotation n...

An algorithm for obtaining rigorous results concerning the existence of chaotic invariant sets of dynamical systems generated by non-autonomous, time periodic differential equations with strong expansion is presented. The result is based on a new theoretical approach to the computation of the homology of the Poincaré map. A concrete numerical example concerning a time-periodic differential equa...

We describe and characterize rigorously the chaotic behavior of the sine– Gordon equation. The existence of invariant manifolds and the persistence of homoclinic orbits for a perturbed sine–Gordon equation are established. We apply a geometric method based on Mel’nikov’s analysis to derive conditions for the transversal intersection of invariant manifolds of a hyperbolic point of the perturbed ...

Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincaré recurrences for a rotation map: only three distinct revival times can occur, with specified weights. A link is thus established between quantum revivals and recurrences in a coarse-grained discrete-time dynamical system.

We study a generalization of the familiar Poincaré map, first implicitely introduced by N N Nekhoroshev in his study of persistence of invariant tori in hamiltonian systems, and discuss some of its properties and applications. In particular, we apply it to study persistence and bifurcation of invariant tori.

We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincaré space, providing a full quantum mechanical characterization of the measured polarization state.

We calculate the discrete-time Conley index of the Poincaré map of a time-periodic ordinary differential equation in an isolated invariant set generated by a periodic isolating segment. As an application, we present results on the existence of bounded solutions of some planar equations.

The problem of nonprehensile manipulation a stick in three-dimensional space using intermittent impulsive forces is considered. objective to juggle the between sequence configurations that are rotationally symmetric about vertical axis. dynamics described by five generalized coordinates and three control inputs. Between two consecutive where inputs applied, conveniently represented Poincaré map...

and Applied Analysis 3 By the same process as in [32], which is based on the analysis of the Poincaré return map defined on some local transversal section of the double homoclinic loop Γ, we obtain the bifurcation equations as follows: