Ladeira, Denis Gouvêa; da Silva, Jafferson Kamphorst Leal Scaling features of a breathing circular billiard. (English) Zbl 1152.70014 J. Phys. A, Math. Theor. 41, No. 36, Article ID 365101, 13 p. (2008). Summary: We investigate the chaotic lowest energy region of a simplified breathing circular billiard, a two-dimensional generalization of Fermi model. When the oscillation amplitude of the breathing boundary is small and we are near the integrable to non-integrable transition, we obtain numerically that average quantities can be described by scaling functions. We also show that the map that describes this model is locally equivalent to Chirikov standard map in the region of phase space near the first invariant spanning curve. Cited in 5 Documents MSC: 70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics 37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010) Keywords:chaotic lowest energy region; Fermi model; Chirikov map PDFBibTeX XMLCite \textit{D. G. Ladeira} and \textit{J. K. L. da Silva}, J. Phys. A, Math. Theor. 41, No. 36, Article ID 365101, 13 p. (2008; Zbl 1152.70014) Full Text: DOI References: [1] Fermi, E.: Phys. rev.. 15, 1169 (1949) [2] Lichtenberg, A. J.; Lieberman, M. A.: Regular and chaotic dynamics. Appl. math. Sci. 38 (1992) · Zbl 0748.70001 [3] Lieberman, M. A.; Lichtenberg, A. J.: Phys. rev. A. 5, 1852 (1971) [4] R. Douady, 1982. Applications du théorème des tores invariants, Thèse de 3ème Cycle, Univ. Paris VII [5] Pustil’nikov, L. D.: Russ. acad. Sci. sb. Math.. 82, No. 1, 231 (1995) [6] Lichtenberg, A. J.; Lieberman, M. A.; Cohen, R. H.: Physica D. 1, 291 (1980) [7] Karlis, A. K.; Diakonos, F. K.; Constantoudis, V.; Schmelcher, P.: Phys. rev. Lett.. 97, 194102 (2006) [8] Leonel, E. D.; Mcclintock, P. V. E.: J. phys. A. 38, 823 (2005) · Zbl 1076.37536 [9] Leonel, E. D.; Mcclintock, P. V. E.: J. phys. A. 38, L425 (2005) · Zbl 1076.37536 [10] Leonel, E. D.; Da Silva, J. K. L.: Physica A. 323, 181 (2003) · Zbl 1073.70518 [11] Karner, G.: J. stat. Phys.. 77, 867 (1994) [12] Dembinski, S. T.; Makowski, A. J.; Peplowski, P.: Phys. rev. Lett.. 70, 1093 (1993) [13] José, J. V.; Cordery, R.: Phys. rev. Lett.. 56, 290 (1986) [14] Saitô, N.; Hirooka, H.; Ford, J.; Vivaldi, F.; Walker, G. H.: Physica D. 5, 273 (1982) [15] Canale, E.; Markarian, R.; Kamphorst, S. O.; De Carvalho, S. P.: Physica D. 115, 189 (1998) [16] Loskutov, A.; Ryabov, A. B.; Akinshin, L. G.: J. phys. A. 33, 7973 (2000) [17] Loskutov, A.; Ryabov, A. B.: J. stat. Phys.. 108, 995 (2002) [18] Loskutov, A.; Ryabov, A. B.; Akinshin, L. G.: J. exp. Theor. phys.. 89, 966 (1999) [19] De Carvalho, R. Egydio; Sousa, F. C.; Leonel, E. D.: Phys. rev. E.. 73, 066229 (2006) [20] De Carvalho, R. Egydio; De Sousa, F. C.; Leonel, E. D.: J. phys. A. 39, 3561 (2006) [21] Kamphorst, S. O.; Leonel, E. D.; Da Silva, J. K. L.: J. phys. A. 40, F887 (2007) · Zbl 0978.37056 [22] Leonel, E. D.; Da Silva, J. K. L.; Kamphorst, S. O.: Physica A. 331, 435 (2004) · Zbl 0978.37056 [23] Da Silva, J. K. L.; Ladeira, D. G.; Leonel, E. D.; Mcclintock, P. V. E.; Kamphorst, S. O.: Braz. J. Phys.. 36, 700 (2006) [24] Leonel, E. D.; Mcclintock, P. V. E.; Da Silva, J. K. L.: Phys. rev. Lett.. 93, 14101 (2004) [25] Ladeira, D. G.; Da Silva, J. K. L.: Phys. rev. E. 73, 026201 (2006) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.