Apparent fractal dimensions in conservative dynamical systems
作者： Giancarlo Benettin , Danilo Casati , Luigi Galgani , Antonio Giorgilli , Luisella Sironi
DOI: 10.1016/0375-9601(86)90318-X
关键词:
摘要: Abstract For conservative dynamical systems, the invariant sets which are in a sense analog of strange attractors dissipative namely closures homoclinic orbits hyperbolic points, known to have general integral dimensions. We show however, working numerically on particular model, that actual numerical estimates for perturbations an integrable system will necessarily exhibit apparent fractal dimension, be effective one all practical purpose. A simple scheme interpretation is also given.
harvard.edu
elsevier.com
sci-hub.se 参考文章(22)
R.S. Mackay, J.D. Meiss, I.C. Percival, Transport in Hamiltonian systems Physica D: Nonlinear Phenomena. ,vol. 13, pp. 55- 81 ,(1984) , 10.1016/0167-2789(84)90270-7
G. Benettin, L. Galgani, A. Giorgilli, Further results on universal properties in conservative dynamical systems Lettere Al Nuovo Cimento. ,vol. 29, pp. 163- 166 ,(1980) , 10.1007/BF02743372
Antonio Giorgilli, Danilo Casati, Luisella Sironi, Luigi Galgani, An efficient procedure to compute fractal dimensions by box counting Physics Letters A. ,vol. 115, pp. 202- 206 ,(1986) , 10.1016/0375-9601(86)90465-2
Celso Grebogi, Steven W. McDonald, Edward Ott, James A. Yorke, Exterior dimension of fat fractals Physics Letters A. ,vol. 110, pp. 1- 4 ,(1985) , 10.1016/0375-9601(85)90220-8
Edward Ott, Strange attractors and chaotic motions of dynamical systems Reviews of Modern Physics. ,vol. 53, pp. 655- 671 ,(1981) , 10.1103/REVMODPHYS.53.655
R. Badii, A. Politi, Hausdorff Dimension and Uniformity factor of strange attractors Physical Review Letters. ,vol. 52, pp. 1661- 1664 ,(1984) , 10.1103/PHYSREVLETT.52.1661
Yu G Borisovich, V G Zvyagin, Yu I Sapronov, NON-LINEAR FREDHOLM MAPS AND THE LERAY-SCHAUDER THEORY Russian Mathematical Surveys. ,vol. 32, pp. 1- 54 ,(1977) , 10.1070/RM1977V032N04ABEH001638
Giancarlo Benettin, Luigi Galgani, Antonio Giorgilli, Exponential law for the equipartition times among translational and vibrational degrees of freedom Physics Letters A. ,vol. 120, pp. 23- 27 ,(1987) , 10.1016/0375-9601(87)90258-1
Marco Pettini, Angelo Vulpiani, Possible failure of Arnold diffusion in nonlinear hamiltonian systems with more than two degrees of freedom Physics Letters A. ,vol. 106, pp. 207- 211 ,(1984) , 10.1016/0375-9601(84)91009-0
P. Grassberger, On the fractal dimension of the Henon attractor Physics Letters A. ,vol. 97, pp. 224- 226 ,(1983) , 10.1016/0375-9601(83)90752-1