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Volumn 39, Issue 7, 1998, Pages 3783-3804

Hard chaos in magnetic billiards (on the hyperbolic plane)

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EID: 0039400320     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532468     Document Type: Article
Times cited : (7)

References (34)
  • 1
    • 84927896522 scopus 로고
    • Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards
    • Ya. G. Sinai, "Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards," Russ. Math. Surv. 25, 137-189 (1970); Usp. Mat. Nauk 25, 141-192 (1970).
    • (1970) Russ. Math. Surv. , vol.25 , pp. 137-189
    • Sinai, Y.G.1
  • 2
    • 84927896522 scopus 로고
    • Ya. G. Sinai, "Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards," Russ. Math. Surv. 25, 137-189 (1970); Usp. Mat. Nauk 25, 141-192 (1970).
    • (1970) Usp. Mat. Nauk , vol.25 , pp. 141-192
  • 3
    • 0011626535 scopus 로고
    • On the ergodic properties of some billiards
    • L. A. Bunimovich, "On the ergodic properties of some billiards," Funct. Anal. Appl. 8, 73-74 (1974).
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 73-74
    • Bunimovich, L.A.1
  • 4
    • 29444443343 scopus 로고
    • On the ergodic properties of nowhere dispersing billiards
    • L. A. Bunimovich, "On the ergodic properties of nowhere dispersing billiards," Commun. Math. Phys. 65, 295-312 (1979).
    • (1979) Commun. Math. Phys. , vol.65 , pp. 295-312
    • Bunimovich, L.A.1
  • 6
    • 0003255969 scopus 로고
    • Chaos in classical and quantum mechanics
    • Springer-Verlag, Berlin
    • M. C. Gutzwiller, "Chaos in classical and quantum mechanics," Vol. 1 of Interdisciplinary Applied Mathematics (Springer-Verlag, Berlin, 1990).
    • (1990) Interdisciplinary Applied Mathematics , vol.1
    • Gutzwiller, M.C.1
  • 7
    • 0002998341 scopus 로고
    • Les surfaces à courbures opposées et leurs lignes geodésiques
    • J. Hadamard, "Les surfaces à courbures opposées et leurs lignes geodésiques," J. Math. pure Appl. 5, 27-73 (1898).
    • (1898) J. Math. Pure Appl. , vol.5 , pp. 27-73
    • Hadamard, J.1
  • 10
    • 0039839715 scopus 로고
    • Ein mechanisches system mit quasiergodischen Bahnen
    • E. Artin, "Ein mechanisches System mit quasiergodischen Bahnen," Hamburger Math. Abh. 3, 499-503 (1924); in Collected Papers (Addison-Wesley, Reading, MA, 1965), pp. 499-501.
    • (1924) Hamburger Math. Abh. , vol.3 , pp. 499-503
    • Artin, E.1
  • 11
    • 0003946760 scopus 로고
    • Addison-Wesley, Reading, MA
    • E. Artin, "Ein mechanisches System mit quasiergodischen Bahnen," Hamburger Math. Abh. 3, 499-503 (1924); in Collected Papers (Addison-Wesley, Reading, MA, 1965), pp. 499-501.
    • (1965) Collected Papers , pp. 499-501
  • 12
    • 46149132858 scopus 로고
    • Chaos on the pseudosphere
    • N. L. Balazs and A. Voros, "Chaos on the pseudosphere," Phys. Rep. 143, 109-240 (1986).
    • (1986) Phys. Rep. , vol.143 , pp. 109-240
    • Balazs, N.L.1    Voros, A.2
  • 13
    • 0010778232 scopus 로고
    • Transition from Poissonian to Gaussian-orthogonal-ensemble level statistics in a modified Artin's billiard
    • A. Csordás, R. Graham, P. Szépfalusy, and G. Vattay, "Transition from Poissonian to Gaussian-orthogonal-ensemble level statistics in a modified Artin's billiard," Phys. Rev. E 49, 325-332 (1994).
    • (1994) Phys. Rev. E , vol.49 , pp. 325-332
    • Csordás, A.1    Graham, R.2    Szépfalusy, P.3    Vattay, G.4
  • 14
    • 0030518477 scopus 로고    scopus 로고
    • The behaviour of nearby trajectories in magnetic billiards
    • T. Tasnádi, "The behaviour of nearby trajectories in magnetic billiards," J. Math. Phys. 37, 5577-5598 (1996).
    • (1996) J. Math. Phys. , vol.37 , pp. 5577-5598
    • Tasnádi, T.1
  • 15
    • 0040455020 scopus 로고    scopus 로고
    • Hard chaos in magnetic billiards (On the Euclidean plane)
    • T. Tasnádi, "Hard chaos in magnetic billiards (On the Euclidean plane)," Commun. Math. Phys. 187, 597-621 (1997).
    • (1997) Commun. Math. Phys. , vol.187 , pp. 597-621
    • Tasnádi, T.1
  • 16
    • 0001550103 scopus 로고
    • Chaotic scattering in the presence of an external magnetic field
    • W. Breymann, Z. Kovács, and T. Tél, "Chaotic scattering in the presence of an external magnetic field," Phys. Rev. E 50, 1994-2006 (1994).
    • (1994) Phys. Rev. E , vol.50 , pp. 1994-2006
    • Breymann, W.1    Kovács, Z.2    Tél, T.3
  • 17
    • 0000452437 scopus 로고
    • Classical billiards in magnetic fields
    • M. Robnik and M. V. Berry, "Classical billiards in magnetic fields," J. Phys. A 18, 1361-1378 (1985).
    • (1985) J. Phys. A , vol.18 , pp. 1361-1378
    • Robnik, M.1    Berry, M.V.2
  • 18
    • 21144468280 scopus 로고
    • Tangent map for classical billiards in magnetic fields
    • O. Meplan, F. Brut, and C. Gignoux, "Tangent map for classical billiards in magnetic fields," J. Phys. A 26, 237-246 (1993).
    • (1993) J. Phys. A , vol.26 , pp. 237-246
    • Meplan, O.1    Brut, F.2    Gignoux, C.3
  • 19
    • 0030536725 scopus 로고    scopus 로고
    • Integrability and ergodicity of classical billiards in a magnetic field
    • N. Berglund and H. Kunz, "Integrability and ergodicity of classical billiards in a magnetic field," J. Stat. Phys. 83, 81-126 (1996).
    • (1996) J. Stat. Phys. , vol.83 , pp. 81-126
    • Berglund, N.1    Kunz, H.2
  • 20
    • 0006889012 scopus 로고
    • Statistical properties of the energy spectrum of 'gliding' electrons with mixed classical trajectories
    • G. M. Zaslavskiǐ and N. N. Filonenko, "Statistical properties of the energy spectrum of 'gliding' electrons with mixed classical trajectories," Sov. Phys. JETP 38, 317-323 (1974); Zh. Eksp. Teor. Fiz. 65, 643-656 (1973).
    • (1974) Sov. Phys. JETP , vol.38 , pp. 317-323
    • Zaslavskiǐ, G.M.1    Filonenko, N.N.2
  • 21
    • 0038965816 scopus 로고
    • G. M. Zaslavskiǐ and N. N. Filonenko, "Statistical properties of the energy spectrum of 'gliding' electrons with mixed classical trajectories," Sov. Phys. JETP 38, 317-323 (1974); Zh. Eksp. Teor. Fiz. 65, 643-656 (1973).
    • (1973) Zh. Eksp. Teor. Fiz. , vol.65 , pp. 643-656
  • 22
    • 0000210690 scopus 로고
    • On the Landau levels on the hyperbolic plane
    • A. Comtet, "On the Landau levels on the hyperbolic plane," Ann. Phys. (N.Y.) 173, 185-209 (1987).
    • (1987) Ann. Phys. (N.Y.) , vol.173 , pp. 185-209
    • Comtet, A.1
  • 24
    • 0000928980 scopus 로고
    • Principles for the design of billiards with nonvanishing Lyapunov exponents
    • M. Wojtkowsky, "Principles for the design of billiards with nonvanishing Lyapunov exponents," Commun. Math. Phys. 105, 391-414 (1986).
    • (1986) Commun. Math. Phys. , vol.105 , pp. 391-414
    • Wojtkowsky, M.1
  • 25
    • 0002472059 scopus 로고
    • Billiards with Pesin region of measure one
    • R. Markarian, "Billiards with Pesin region of measure one," Commun. Math. Phys. 118, 87-97 (1988).
    • (1988) Commun. Math. Phys. , vol.118 , pp. 87-97
    • Markarian, R.1
  • 26
    • 0001703406 scopus 로고
    • Using integrability to produce chaos: Billiards with positive entropy
    • V. J. Donnay, "Using integrability to produce chaos: Billiards with positive entropy," Commun. Math. Phys. 141, 225-257 (1991).
    • (1991) Commun. Math. Phys. , vol.141 , pp. 225-257
    • Donnay, V.J.1
  • 27
    • 0002189261 scopus 로고
    • The modular surface and continued fractions
    • C. Series, "The modular surface and continued fractions," J. London Math. Soc. 2, 69-80 (1985).
    • (1985) J. London Math. Soc. , vol.2 , pp. 69-80
    • Series, C.1
  • 28
    • 0001153965 scopus 로고
    • Coding chaotic billiards
    • M-J. Giannoni and D. Ullmo, "Coding chaotic billiards," Physica 41, 371-390 (1990).
    • (1990) Physica , vol.41 , pp. 371-390
    • Giannoni, M.-J.1    Ullmo, D.2
  • 29
    • 0008151644 scopus 로고
    • A criterion for the positivity of the Lyapunov characteristic exponent
    • E. Cornelis and M. Wojtkowsky, "A criterion for the positivity of the Lyapunov characteristic exponent," Ergod. Theor. Dyn. Syst. 4, 527-539 (1984).
    • (1984) Ergod. Theor. Dyn. Syst. , vol.4 , pp. 527-539
    • Cornelis, E.1    Wojtkowsky, M.2
  • 30
    • 0000176923 scopus 로고
    • Invariant families of cones and Lyapunov exponents
    • M. Wojtkowsky, "Invariant families of cones and Lyapunov exponents," Ergod. Theor. Dyn. Syst. 5, 145-161 (1985).
    • (1985) Ergod. Theor. Dyn. Syst. , vol.5 , pp. 145-161
    • Wojtkowsky, M.1
  • 31
    • 0000543733 scopus 로고
    • The multiplicative ergodic theorem. The Lyapunov characteristic numbers of a dynamical system
    • V. I. Oseledec, "The multiplicative ergodic theorem. The Lyapunov characteristic numbers of a dynamical system," Trans. Moscow Math. Soc. 19, 197-231 (1968).
    • (1968) Trans. Moscow Math. Soc. , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 32
    • 84961291543 scopus 로고
    • Lyapunov characteristic exponents and smooth ergodic theory
    • Ya. B. Pesin, "Lyapunov characteristic exponents and smooth ergodic theory," Russ. Math. Surveys 32, 55-114 (1977).
    • (1977) Russ. Math. Surveys , vol.32 , pp. 55-114
    • Pesin, Y.B.1
  • 33
    • 0003280184 scopus 로고
    • Invariant manifolds, entropy and billiards; smooth maps with singularities
    • Springer-Verlag, Berlin, in collaboration with F. Ledrappier and F. Przytycki
    • A. Katok and J.-M. Strelcyn, "Invariant manifolds, entropy and billiards; smooth maps with singularities," Vol. 1222 of Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1986), in collaboration with F. Ledrappier and F. Przytycki.
    • (1986) Lecture Notes in Mathematics , vol.1222
    • Katok, A.1    Strelcyn, J.-M.2
  • 34
    • 0000232377 scopus 로고
    • On the K-property of some planar hyperbolic billiards
    • D. Szász, "On the K-property of some planar hyperbolic billiards," Commun. Math. Phys. 145, 595-604 (1992).
    • (1992) Commun. Math. Phys. , vol.145 , pp. 595-604
    • Szász, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.