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Volumn 241, Issue 5, 2012, Pages 514-518

The Arnold cat map, the Ulam method and time reversal

Author keywords

Dynamical chaos; Markov chains; Statistical description

Indexed keywords

CHAINS; MARKOV PROCESSES;

EID: 84855758917     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2011.11.012     Document Type: Article
Times cited : (20)

References (25)
  • 3
    • 0012097571 scopus 로고
    • A universal instability of many-dimensional oscillator systems
    • B.V. Chirikov A universal instability of many-dimensional oscillator systems Phys. Rep. 52 1979 263
    • (1979) Phys. Rep. , vol.52 , pp. 263
    • Chirikov, B.V.1
  • 5
    • 0036591029 scopus 로고    scopus 로고
    • Quantum computer inverting time arrow for macroscopic systems
    • B. Georgeot, and D.L. Shepelyansky Quantum computer inverting time arrow for macroscopic systems Eur. Phys. J. D 19 2002 263
    • (2002) Eur. Phys. J. D , vol.19 , pp. 263
    • Georgeot, B.1    Shepelyansky, D.L.2
  • 6
    • 0000725751 scopus 로고
    • Interscience Tracs in Pure and Applied Mathematics Interscience New York
    • S.M. Ulam A Collection of Mathematical Problems Interscience Tracs in Pure and Applied Mathematics vol. 8 1960 Interscience New York 73
    • (1960) A Collection of Mathematical Problems , vol.8 VOL. , pp. 73
    • Ulam, S.M.1
  • 7
    • 0012526528 scopus 로고
    • Rasprostranenie zakona bol'shih chisel na velichiny, zavisyaschie drug ot druga
    • 0XUB (in Russian) [English trans.: extension of the limit theorems of probability theory to a sum of variables connected in a chain reprinted in Appendix B of: R.A. Howard Dynamic Probabilistic Systems, Volume 1: Markov Models, Dover Publ. (2007)]
    • A.A. Markov Rasprostranenie zakona bol'shih chisel na velichiny, zavisyaschie drug ot druga Izv. Fiz.-Mat. Obsch. Kazan. Univ. Ser. 2 15 1906 135 0XUB (in Russian) [English trans.: extension of the limit theorems of probability theory to a sum of variables connected in a chain reprinted in Appendix B of: R.A. Howard Dynamic Probabilistic Systems, Volume 1: Markov Models, Dover Publ. (2007)]
    • (1906) Izv. Fiz.-Mat. Obsch. Kazan. Univ. Ser. 2 , vol.15 , pp. 135
    • Markov, A.A.1
  • 9
    • 0001062377 scopus 로고
    • Finite approximation for the PerronFrobenius operator, a solution to Ulam's conjecture
    • T.-Y. Li Finite approximation for the PerronFrobenius operator, a solution to Ulam's conjecture J. Approx. Theory 17 1976 177
    • (1976) J. Approx. Theory , vol.17 , pp. 177
    • Li, T.-Y.1
  • 10
    • 0041972697 scopus 로고    scopus 로고
    • RuellePerronFrobenius spectrum for Anosov maps
    • M. Blank, G. Keller, and C. Liverani RuellePerronFrobenius spectrum for Anosov maps Nonlinearity 15 2002 1905
    • (2002) Nonlinearity , vol.15 , pp. 1905
    • Blank, M.1    Keller, G.2    Liverani, C.3
  • 11
    • 51849091830 scopus 로고    scopus 로고
    • Rigorous numerical approximation of RuellePerronFrobenius operators and topological pressure of expanding maps
    • D. Terhesiu, and G. Froyland Rigorous numerical approximation of RuellePerronFrobenius operators and topological pressure of expanding maps Nonlinearity 21 2008 1953
    • (2008) Nonlinearity , vol.21 , pp. 1953
    • Terhesiu, D.1    Froyland, G.2
  • 12
    • 77949683737 scopus 로고    scopus 로고
    • Google matrix, dynamical attractors and Ulam networks
    • D.L. Shepelyansky, and O.V. Zhirov Google matrix, dynamical attractors and Ulam networks Phys. Rev. E 81 2010 036213
    • (2010) Phys. Rev. e , vol.81 , pp. 036213
    • Shepelyansky, D.L.1    Zhirov, O.V.2
  • 13
    • 77954819505 scopus 로고    scopus 로고
    • Ulam method for the Chirikov standard map
    • K.M. Frahm, and D.L. Shepelyansky Ulam method for the Chirikov standard map Eur. Phys. J. B 76 2010 57
    • (2010) Eur. Phys. J. B , vol.76 , pp. 57
    • Frahm, K.M.1    Shepelyansky, D.L.2
  • 14
    • 25544477348 scopus 로고
    • Scaling in multifractals: Discretization of an eigenvalue problem
    • Z. Kovács, and T. Tél Scaling in multifractals: discretization of an eigenvalue problem Phys. Rev. A 40 1989 4641
    • (1989) Phys. Rev. A , vol.40 , pp. 4641
    • Kovács, Z.1    Tél, T.2
  • 15
    • 34548831423 scopus 로고    scopus 로고
    • Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension
    • G. Froyland, R. Murray, and D. Terhesiu Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension Phys. Rev. E 76 2007 036702
    • (2007) Phys. Rev. e , vol.76 , pp. 036702
    • Froyland, G.1    Murray, R.2    Terhesiu, D.3
  • 16
    • 77950437999 scopus 로고    scopus 로고
    • Google matrix and Ulam networks of intermittency maps
    • L. Ermann, and D.L. Shepelyansky Google matrix and Ulam networks of intermittency maps Phys. Rev. E 81 2010 036221
    • (2010) Phys. Rev. e , vol.81 , pp. 036221
    • Ermann, L.1    Shepelyansky, D.L.2
  • 17
    • 67650066712 scopus 로고    scopus 로고
    • Almost-invariant sets and invariant manifoldsconnecting probabilistic and geometric descriptions of coherent structures in flows
    • G. Froyland, and K. Padberg Almost-invariant sets and invariant manifoldsconnecting probabilistic and geometric descriptions of coherent structures in flows Physica D 238 2009 1507
    • (2009) Physica D , vol.238 , pp. 1507
    • Froyland, G.1    Padberg, K.2
  • 18
    • 77954564189 scopus 로고    scopus 로고
    • Ulam method and fractal Weyl law for PerronFrobenius operators
    • L. Ermann, and D.L. Shepelyansky Ulam method and fractal Weyl law for PerronFrobenius operators Eur. Phys. J. B 75 2010 299
    • (2010) Eur. Phys. J. B , vol.75 , pp. 299
    • Ermann, L.1    Shepelyansky, D.L.2
  • 20
    • 0035805968 scopus 로고    scopus 로고
    • Stable quantum computation of unstable classical chaos
    • B. Georgeot, and D.L. Shepelyansky Stable quantum computation of unstable classical chaos Phys. Rev. Lett. 86 2001 5393
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 5393
    • Georgeot, B.1    Shepelyansky, D.L.2
  • 21
    • 48749147456 scopus 로고
    • Some statistical properties of simple classically stochastic quantum systems
    • D.L. Shepelyansky Some statistical properties of simple classically stochastic quantum systems Physica D 8 1983 208
    • (1983) Physica D , vol.8 , pp. 208
    • Shepelyansky, D.L.1
  • 22
    • 33750117937 scopus 로고    scopus 로고
    • Big entropy fluctuations in statistical equilibrium: The macroscopic kinetics
    • (in Russian): Zh. Eksp. Teor. Fiz. 120 (1) (2001), 214]
    • B.V. Chirikov, and O.V. Zhirov Big entropy fluctuations in statistical equilibrium: the macroscopic kinetics JETP 93 2001 188 (in Russian): Zh. Eksp. Teor. Fiz. 120 (1) (2001), 214]
    • (2001) JETP , vol.93 , pp. 188
    • Chirikov, B.V.1    Zhirov, O.V.2
  • 23
    • 0001460865 scopus 로고
    • Dynamical stochasticity in classical and quantum mechanics
    • [Sec. C-Math. Phys. Rev., Ed. S.P.Novikov, vol. 2, Harwood Acad. Publ., Chur, Switzerland (1981)]
    • B.V. Chirikov, F.M. Izrailev, and D.L. Shepelyansky Dynamical stochasticity in classical and quantum mechanics Sov. Sci. Rev. C 2 1981 209 [Sec. C-Math. Phys. Rev., Ed. S.P.Novikov, vol. 2, Harwood Acad. Publ., Chur, Switzerland (1981)]
    • (1981) Sov. Sci. Rev. C , vol.2 , pp. 209
    • Chirikov, B.V.1    Izrailev, F.M.2    Shepelyansky, D.L.3
  • 24
    • 0004809980 scopus 로고
    • Quantum chaos: Localization vs. ergodicity
    • Quantum chaos: localization vs. ergodicity Physica D 33 1988 77
    • (1988) Physica D , vol.33 , pp. 77
  • 25
    • 21344493594 scopus 로고
    • Molecular dynamics and time reversibility
    • D. Levesque, and L. Verlet Molecular dynamics and time reversibility J. Stat. Phys. 72 1993 519
    • (1993) J. Stat. Phys. , vol.72 , pp. 519
    • Levesque, D.1    Verlet, L.2


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