Sticky orbits of chaotic Hamiltonian dynamics
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.
KeywordsChaos fractals dimensions Poincaré recurrences
Unable to display preview. Download preview PDF.
- U. Frisch and G. Parisi, in Turbulence and Predictability of Geophysical Flows and Climate Dynamics, edited by M. Ghill, R. Benzi, and G. Parisi (North-Holland, Amsterdam, 1985).Google Scholar
- M.H. Jensen, L.P. Kadanoff, A. Libshaber, I. Procaccia, and J. Stavans, Phys. Rev. Lett. 55, 439 (1985)Google Scholar
- L. Barreira, J. Schmeling, Sets of “non-typical” points have full topological entropy and full Hausdorff dimension, Preprint, (1997).Google Scholar
- E.B. Vul, Ya.G. Sinai, and K.M. Khanin, in Advanced Series in Nonlinear Dynamics 1: Dynamical Systems (ed. by Ya.G. Sinai), World Scientific, Singapore, 501 (1991).Google Scholar
- V.K. Melnikov, in Transport, Chaos and Plasma Physics 2 (eds. S. Benkadda, F. Doveil, Y. Elskens) World Scientific, Singapore, 142, (1996).Google Scholar
- G.M. Zaslavsky and M. Edelman, Phys. Rev. E 56, ... (1997).Google Scholar
- Y. Pesin, Dimension Theory in Dynamical Systems: Rigorous Results and Applicaiton, University of Chicago Press, Chicago, (1997).Google Scholar
- C. Carathèodory, Nach. Ges. Wiss. Götingen, 406 (1914).Google Scholar