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1. G. A. Luna-Acosta, J. A. Méndez-Bermúdez, P. Seba, and K. N. Pichugin, “Classical versus quantum structure of the scattering probability matrix: chaotic waveguides,” Physical Review E, vol. 65, no. 4, Article ID 046605, 8 pages, 2002. View at Publisher · View at Google Scholar
2. G. M. Zaslavsky, “Chaos, fractional kinetics, and anomalous transport,” Physics Reports A, vol. 371, no. 6, pp. 461–580, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
3. D. G. Ladeira and J. K. L. da Silva, “Scaling properties of a simplified bouncer model and of Chirikov's standard map,” Journal of Physics A, vol. 40, no. 38, pp. 11467–11483, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
4. R. Venegeroles, “Calculation of superdiffusion for the Chirikov-Taylor model,” Physical Review Letters, vol. 101, no. 5, Article ID 054102, 4 pages, 2008. View at Publisher · View at Google Scholar
5. S. M. Soskin, R. Mannella, and O. M. Yevtushenko, “Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices,” Physical Review E, vol. 77, no. 3, Article ID 036221, 29 pages, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
6. F. R. N. Koch, F. Lenz, C. Petri, F. K. Diakonos, and P. Schmelcher, “Dynamical trapping and chaotic scattering of the harmonically driven barrier,” Physical Review E, vol. 78, no. 5, Article ID 056204, 13 pages, 2008. View at Publisher · View at Google Scholar
7. J. E. Howard, A. J. Lichtenberg, M. A. Lieberman, and R. H. Cohen, “Four-dimensional mapping model for two-frequency electron cyclotron resonance heating,” Physica D, vol. 20, no. 2-3, pp. 259–284, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
8. F. Saif, “Dynamical localization and signatures of classical phase space,” Physics Letters A, vol. 274, no. 3-4, pp. 98–103, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
9. F. Saif, I. Bialynicki-Birula, M. Fortunato, and W. P. Schleich, “Fermi accelerator in atom optics,” Physical Review A, vol. 58, no. 6, pp. 4779–4783, 1998. View at Publisher · View at Google Scholar · View at Scopus
10. G. A. Luna-Acosta, K. Na, L. E. Reichl, and A. Krokhin, “Band structure and quantum Poincaré sections of a classically chaotic quantum rippled channel,” Physical Review E, vol. 53, no. 4, pp. 3271–3283, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
11. A. M. O. de Almeida, Sistemas Hamiltonianos—Caos e Quantização, Editora da Unicamp, Unicamp, Brazil, 3rd edition, 1995.
12. G. A. Luna-Acosta, G. Orellana-Rivadeneyra, A. Mendoza-Galván, and C. Jung, “Chaotic classical scattering and dynamics in oscillating 1-D potential wells,” Chaos, Solitons & Fractals, vol. 12, no. 2, pp. 349–363, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
13. J. L. Mateos, “Traversal-time distribution for a classical time-modulated barrier,” Physics Letters A, vol. 256, no. 2-3, pp. 113–121, 1999. View at Publisher · View at Google Scholar · View at Scopus
14. E. D. Leonel and P. V. E. McClintock, “Chaotic properties of a time-modulated barrier,” Physical Review E, vol. 70, no. 1, Article ID 016214, 11 pages, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
15. E. D. Leonel and P. V. E. McClintock, “Dynamical properties of a particle in a time-dependent double-well potential,” Journal of Physics A, vol. 37, no. 38, pp. 8949–8968, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
16. E. D. Leonel and P. V. McClintock, “Scaling properties for a classical particle in a time-dependent potential well,” Chaos, vol. 15, no. 3, Article ID 033701, 7 pages, 2005. View at Zentralblatt MATH
17. K. Ullmann and I. L. Caldas, “A symplectic mapping for the ergodic magnetic limiter and its dynamical analysis,” Chaos, Solitons & Fractals, vol. 11, no. 13, pp. 2129–2140, 2000. View at Zentralblatt MATH · View at MathSciNet
18. I. L. Caldas, J. M. Pereira, K. Ullmann, and R. L. Viana, “Magnetic field line mappings for a tokamak with ergodic limiters,” Chaos, Solitons & Fractals, vol. 7, no. 7, pp. 991–1010, 1996. View at Publisher · View at Google Scholar · View at Scopus
19. S. S. Abdullaev and G. M. Zaslavsky, “Application of the separatrix map to study perturbed magnetic field lines near the separatrix,” Physics of Plasmas, vol. 3, no. 2, pp. 516–528, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
20. A. Punjabi, H. Ali, and A. Boozer, “Symmetric simple map for a single-null divertor tokamak,” Physics of Plasmas, vol. 4, no. 2, pp. 337–346, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
21. J. Koiller, R. Markarian, S. O. Kamphorst, and S. P. de Carvalho, “Static and time-dependent perturbations of the classical elliptical billiard,” Journal of Statistical Physics, vol. 83, no. 1-2, pp. 127–143, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
22. A. Loskutov and A. Ryabov, “Particle dynamics in time-dependent stadium-like billiards,” Journal of Statistical Physics, vol. 108, no. 5-6, pp. 995–1014, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
23. D. G. Ladeira and J. K. L. da Silva, “Scaling features of a breathing circular billiard,” Journal of Physics A, vol. 41, no. 36, Article ID 365101, 13 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
24. E. D. Leonel, “Corrugated waveguide under scaling investigation,” Physical Review Letters, vol. 98, no. 11, Article ID 114102, 4 pages, 2007. View at Publisher · View at Google Scholar
25. A. F. Rabelo and E. D. Leonel, “Finding invariant tori in the problem of a periodically corrugated waveguide,” Brazilian Journal of Physics, vol. 38, no. 1, pp. 54–57, 2008. View at Publisher · View at Google Scholar · View at Scopus
26. A. L. Virovlyansky and G. M. Zaslavsky, “Evaluation of the smoothed interference pattern under conditions of ray chaos,” Chaos, vol. 10, no. 1, pp. 211–223, 2000. View at Publisher · View at Google Scholar · View at PubMed · View at Zentralblatt MATH · View at MathSciNet
27. I. P. Smirnov, A. L. Virovlyansky, and G. M. Zaslavsky, “Theory and applications of ray chaos to underwater acoustics,” Physical Review E, vol. 64, no. 3, Article ID 036221, 20 pages, 2001. View at Publisher · View at Google Scholar
28. A. Iomin and Yu. Bliokh, “Wave localization as a manifestation of ray chaos in underwater acoustics,” Communications in Nonlinear Science and Numerical Simulation, vol. 8, no. 3-4, pp. 389–399, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
29. B. Huckestein, R. Ketzmerick, and C. H. Lewenkopf, “Quantum transport through ballistic cavities: soft vs hard quantum chaos,” Physical Review Letters, vol. 84, no. 24, pp. 5504–5507, 2000. View at Publisher · View at Google Scholar · View at Scopus
30. B. Huckestein, R. Ketzmerick, and C. H. Lewenkopf, “Erratum: quantum transport through ballistic cavities: soft vs hard quantum chaos,” Physical Review Letters, vol. 87, no. 11, Article ID 119901, 2 pages, 2001. View at Publisher · View at Google Scholar
31. L. P. Kouwenhoven, F. W. J. Hekking, B. J. van Wees, C. J. P. M. Harmans, C. E. Timmering, and C. T. Foxon, “Transport through a finite one-dimensional crystal,” Physical Review Letters, vol. 65, no. 3, pp. 361–364, 1990. View at Publisher · View at Google Scholar · View at Scopus
32. M. Leng and C. S. Lent, “Recovery of quantized ballistic conductance in a periodically modulated channel,” Physical Review Letters, vol. 71, no. 1, pp. 137–140, 1993. View at Publisher · View at Google Scholar · View at Scopus
33. G. A. Luna-Acosta, J. A. Méndez-Bermúdez, and F. M. Izrailev, “Periodic chaotic billiards: quantum-classical correspondence in energy space,” Physical Review E, vol. 64, no. 3, Article ID 036206, 18 pages, 2001. View at Publisher · View at Google Scholar
34. G. A. Luna-Acosta, J. A. Méndez-Bermúdez, and F. M. Izrailev, “Quantum-classical correspondence for local density of states and eigenfunctions of a chaotic periodic billiard,” Physics Letters A, vol. 274, no. 5-6, pp. 192–199, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
35. G. B. Akguc and L. E. Reichl, “Direct scattering processes and signatures of chaos in quantum waveguides,” Physical Review E, vol. 67, no. 4, Article ID 046202, 10 pages, 2003. View at Publisher · View at Google Scholar
36. R. B. Hwang, “Negative group velocity and anomalous transmission in a one-dimensionally periodic waveguide,” IEEE Transactions on Antennas and Propagation, vol. 54, no. 2, pp. 755–759, 2006. View at Publisher · View at Google Scholar
37. L. A. Bunimovich, “On the ergodic properties of nowhere dispersing billiards,” Communications in Mathematical Physics, vol. 65, no. 3, pp. 295–312, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
38. Y. G. Sinai, “Dynamical systems with elastic reflections,” Russian Mathematical Surveys, vol. 25, no. 2, pp. 137–189, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
39. M. V. Berry, “Regularity and chaos in classical mechanics, illustrated by three deformations of a circular “billiard”,” European Journal of Physics, vol. 2, no. 2, pp. 91–102, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
40. S. O. Kamphorst and S. P. de Carvalho, “Bounded gain of energy on the breathing circle billiard,” Nonlinearity, vol. 12, no. 5, pp. 1363–1371, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
41. M. Robnik, “Classical dynamics of a family of billiards with analytic boundaries,” Journal of Physics A, vol. 16, no. 17, pp. 3971–3986, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
42. M. Robnik and M. V. Berry, “Classical billiards in magnetic fields,” Journal of Physics A, vol. 18, no. 9, pp. 1361–1378, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
43. R. Markarian, S. O. Kamphorst, and S. P. de Carvalho, “Chaotic properties of the elliptical stadium,” Communications in Mathematical Physics, vol. 174, no. 3, pp. 661–679, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
44. J.-P. Eckmann and D. Ruelle, “Ergodic theory of chaos and strange attractors,” Reviews of Modern Physics, vol. 57, no. 3, pp. 617–656, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
45. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, vol. 38 of Applied Mathematical Sciences, Springer, New York, NY, USA, 2nd edition, 1992. View at MathSciNet
46. E. D. Leonel and P. V. E. McClintock, “A hybrid Fermi-Ulam-bouncer model,” Journal of Physics A, vol. 38, no. 4, pp. 823–839, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
47. A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, UK, 1985.
48. E. D. Leonel, P. V. E. McClintock, and J. K. L. da Silva, “Fermi-Ulam accelerator model under scaling analysis,” Physical Review Letters, vol. 93, no. 1, Article ID 014101, 4 pages, 2004. View at Publisher · View at Google Scholar
49. E. Fermi, “On the origin of the cosmic radiation,” Physical Review, vol. 75, no. 8, pp. 1169–1174, 1949. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
50. M. A. Lieberman and A. J. Lichtenberg, “Stochastic and adiabatic behavior of particles accelerated by periodic forces,” Physical Review A, vol. 5, no. 4, pp. 1852–1866, 1972. View at Publisher · View at Google Scholar · View at Scopus
51. L. D. Pustyl'nikov, “On Ulam's problem,” Theoretical and Mathematical Physics, vol. 57, no. 1, pp. 1035–1038, 1983. View at Publisher · View at Google Scholar · View at Scopus
52. A. J. Lichtenberg, M. A. Lieberman, and R. H. Cohen, “Fermi acceleration revisited,” Physica D, vol. 1, no. 3, pp. 291–305, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
53. G. Karner, “The simplified Fermi accelerator in classical and quantum mechanics,” Journal of Statistical Physics, vol. 77, no. 3-4, pp. 867–879, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
54. S. T. Dembiński, A. J. Makowski, and P. Pepłowski, “Quantum bouncer with chaos,” Physical Review Letters, vol. 70, no. 8, pp. 1093–1096, 1993. View at Publisher · View at Google Scholar · View at Scopus