Regular and chaotic motion in softened gravitational systems

Phase Synchronization in Regular and Chaotic Systems

In this contribution we present a brief introduction to the theory of synchronization of self-sustained oscillators. Classical results for synchronization of periodic motions and eeects of noise on this process are reviewed and compared with recently found phase synchronization phenomena in chaotic oscillators. The basic notions of phase and frequency locking are reconsidered within a common fr...

A Fast and Reliable Method for Distinguishing Regular from Chaotic Motion in Hamiltonian Systems

We describe the recently introduced method of the Smaller Alignment Index (SALI) for distinguishing ordered from chaotic motion in conservative dynamical systems and apply it to Hamiltonian systems of 2 degrees of freedom. We show the effectiveness and the speed of the method in the determination of the dynamical nature of orbits of Hamiltonian systems that possess a very rich structure on a Po...

Regular and Chaotic Dynamics of Triaxial Stellar Systems

We use Laskar’s frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of ∼ 10 orbits, we numerically compute the three fundamental frequencies of the motion, allowing us to map out the Arnold web. We also compute diffusion rates of stochastic orbits in frequency space. The objects of fundamental importance in str...

Resonance-assisted tunneling in mixed regular-chaotic systems

Periodic Orbit Quantization of Mixed Regular Chaotic Systems

A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence function up to, in principle, infinite length. As in our recent work the recurrence signal is inverted by means of a high resolution spectral analyzer (harmonic i...