Related papers: Hamiltonian mappings and circle packing phase spac…
We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of three different phase space geometries (planar, hyperbolic or…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For…
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant…
The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their…
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…
It is well known that typical Hamiltonian systems have divided phase space consisting of regions with regular dynamics on KAM tori and region(s) with chaotic dynamics called chaotic sea(s). This complex structure makes rigorous analysis of…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincar\'e map, is…
The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take…
Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincar\'{e} recurrences for a rotation map: only three distinct…
Several mean-field theories predict that Hessian matrices of amorphous solids can be written by using the random matrix in the limit of the large spatial dimensions $d\to\infty$. Motivated by these results, we here propose a way to map a…
We prove quantitative decay estimates of macroscopic quantities generated by the solutions to linear transport equations driven by a general family of Hamiltonians. The associated particle trajectories are all trapped in a compact region of…
The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their…
For a satellite with an irregular shape, which is the common shape among asteroids, the well-known spin-orbit resonance problem could be changed to a spin-orbit coupling problem since a decoupled model does not accurately capture the…
It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a…
We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency…
Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that the latter can be eliminated by inducing suitable geometric phases in the states, by…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…