Statistical properties of chaos demonstrated in a class of one-dimensional maps |
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| Authors: | Csordas Andras Gyorgyi Geza Szepfalusy Peter Tel Tamas |
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| Institution: | Research Institute for Solid State Physics of the Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest, HungaryInstitute for Theoretical Physics, Eotvos University, Puskin u. 5-7, H-1088 Budapest, HungaryInstitute for Solid State Physics, Eotvos University, Muzeum krt. 6-8, H-1088 Budapest, HungaryResearch Institute for Solid State Physics of the Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest, HungaryInstitute for Theoretical Physics, Eotvos University, Puskin u. 5-7, H-1088 Budapest, Hungary. |
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| Abstract: | One-dimensional maps with complete grammar are investigated in both permanent and transient chaotic cases. The discussion focuses on statistical characteristics such as Lyapunov exponent, generalized entropies and dimensions, free energies, and their finite size corrections. Our approach is based on the eigenvalue problem of generalized Frobenius-Perron operators, which are treated numerically as well as by perturbative and other analytical methods. The examples include the universal chaos function relevant near the period doubling threshold. Special emphasis is put on the entropies and their decay rates because of their invariance under the most general class of coordinate changes. Phase-transition-like phenomena at the border state of chaos due to intermittency and super instability are presented. |
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