Statistics of Poincaré recurrences for a class of smooth circle maps

Chaos, Solitons and Fractals

Volumn 23, Issue 5, 2005, Pages 1829-1840

  Buric, Nikola ^a   Rampioni, Aldo ^b   Turchetti, Giorgio ^b  

^a UNIVERSITY OF BELGRADE   (Serbia)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); MATHEMATICAL TRANSFORMATIONS; PERTURBATION TECHNIQUES; PROBABILITY; SET THEORY; SPECTRUM ANALYSIS; STATISTICS; THEOREM PROVING; TOPOLOGY;

CIRCLE MAPS; DIFFEOMORPHISM; ERGODIC SYSTEMS; POINCAŔE RECURRENCES;

CHAOS THEORY;

EID: 9544247742     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(04)00448-5     Document Type: Article

References (26)

1. Chirikov BV, Shepelyansky DI. Asymptotic statistics of Poincaré recurrences in Hamiltonian systems with divided phase space. Phys Rev Lett 1999;82:528.
2. Hirata M, Saussol B, Vaienti S. Statistics of return times: a general framework and new applications. Commun Math Phys 1999;206:33.
3. Ornstein S, Weiss B. Entropy and data compression. IEEE Trans Inf Theory 1993;39:78.
4. Haydn N, Luevano J, Mantica G, Vaienti S. Multifractal properties of return time statistic, 2001 [preprint].
5. Hirata M. Poisson law for dynamical systems with the "self- mixing" condition. Dyn Syst Chaos 1995;1:87.
6. Young LS. Recurrence times and rates of mixing. Israel J Math 1999;110:153.
7. Rampioni A, Turchetti G, Vaienti S. Contribution to the summer school Mathematical Aspects of Quantum Chaos, Bologna, 1-10 September, 2001.
8. Hu H, Rampioni A, Turchetti G, Vaienti S. Polynomial law decay of the return times spectrum for integrable area preserving maps, in preparation.
9. Zaslavsky GM, Edelman M. Weak mixing and anomalous kinetics along filamented surfaces. Chaos 2001;11:295.
10. Buric N, Rampioni A, Turchetti G, Vaienti S. Weak chaos and Poincaré recurrences for area-preserving maps. J Phys A: Math Gen 2003.
11. Slater NB. Gaps and steps for the sequence nθ mod 1. Proc Cambridge Philos Soc 1967;63:1115.
12. Denjoy A. Sur le curbes definies par le equation différentieles a la surface du tore. J Math Pures Appl 1932;11:333.
13. Herman M. Sur la conjugasion différentiable des difféomorphismes du cercle a des rotations. Pub Mat IHES 1979;49:5.
14. Geisel T, Nierwetberg J. Onset of diffusion and universal scaling in chaotic systems. Phys Rev Lett 1981;48:7.
15. Glass L, Perez R. Fine structure of phase-locking. Phys Rev Lett 1982;48:1772.
16. Jensen MH, Bak P, Bohr T. Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps. Phys Rev A 1984;30:1960.
17. Bohr T, Gunaratne G. Scaling for supercritical circle maps: numerical investigation of the onset of bistability and period doubling. Phys Lett A 1985;113:55.
18. Boyland PL. Bifurcations of circle maps: Arnold's tongues, bistability and rotation intervals. Commun Math Phys 1986;106:353.
19. MacKay RS, Tresser C. Transition to topological chaos for circle maps. Physica D 1986;19:206.
20. Rand D, Ostlung S, Sethna J, Siggia ED. Universal transition from quasiperiodicity to chaos in dissipative systems. Phys Rev Lett 1982;49:132.
21. Buric B, Cartwright JR, Piro O, Percival IC. On modular smoothing and scaling functions for mode-locking, Limit laws for entrance times for homeomorphisms of the circle. Phys Lett A 1992;163:63.
22. Bruks KM, Tresser C. A Farey tree organization of locking regions for simple circle maps. Proc Am Math Soc 1996;124:637.
23. Khanin KM. Universal estimates for critical circle maps. Chaos 1991;1:181.
24. Hunt BR, Khanin KM, Sinai YaG, Yorke JA. Fractal properties of critical invariant curves. J Statis Phys 1996;85:261.
25. Buric N, Mudrinic M, Todorovic K. Universal scaling of critical quasiperiodic orbits in a class of twist maps. J Phys A: Math Gen 1998;31:7847.
26. Coelho Z, Faria Ede. Limit laws for entrance times for homeomorphisms of the circle. Israel J Math 1996;93:93.