Sticky orbits of chaotic Hamiltonian dynamics. (English) Zbl 0929.37020
Benkadda, Sadruddin (ed.) et al., Chaos, kinetics and nonlinear dynamics in fluids and plasmas. Proceedings of a workshop, Carry-Le Rouet, France, June 16–21, 1997. Berlin: Springer. Lect. Notes Phys. 511, 59-82 (1998).
Summary: Nonuniformity of the phase space of chaotic Hamiltonian dynamics can result from the existence of a sticky set called “Sticky Riddle” (SR) imbedded into the phase space. Fractal and multifractal properties of SR can be described for some simplified situations. Existence of SR imposes similar stickiness for chaotic orbits when they approach the vicinity of SR. As a result, the orbits reveal behavior with power-like tails in the distribution of Poincaré recurrences and exit times, which is unusual for hyperbolic systems. We exploit the generalized fractal dimension to describe the set of recurrences.
For the entire collection see [Zbl 0896.00027].
For the entire collection see [Zbl 0896.00027].
MSC:
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
