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Volumn 9, Issue 4, 2003, Pages 859-876

Ulam's scheme revisited: Digital modeling of chaotic attractors via micro-perturbations

Author keywords

Computation; Digital arithmetic; Ergodic maps; Expanding maps; Minimal perturbation; Random perturbation; Ulam's scheme

Indexed keywords


EID: 0038739420     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2003.9.859     Document Type: Article
Times cited : (14)

References (22)
  • 2
    • 0000162998 scopus 로고    scopus 로고
    • Random perturbations of chaotic dynamical systems: Stability of the spectrum
    • M. Blanc and G. Keller, Random perturbations of chaotic dynamical systems: stability of the spectrum., Nonlinearity 11 (1998), 1351-1364.
    • (1998) Nonlinearity , vol.11 , pp. 1351-1364
    • Blanc, M.1    Keller, G.2
  • 3
    • 0037778687 scopus 로고
    • Digital modelling of chaotic motion
    • G. Domokos, Digital modelling of chaotic motion, Studia Sci. Math. Hung. 25 (1990), 323-341.
    • (1990) Studia Sci. Math. Hung. , vol.25 , pp. 323-341
    • Domokos, G.1
  • 4
  • 5
    • 0020943209 scopus 로고
    • Strange attractors and chaos in nonlinear mechanics
    • P.J. Holmes and F.C Moon, Strange attractors and chaos in nonlinear mechanics, Trans. ASME Ser.E, J. Appl. Mech. 50 (1983), 1021-1032.
    • (1983) Trans. ASME Ser.E, J. Appl. Mech. , vol.50 , pp. 1021-1032
    • Holmes, P.J.1    Moon, F.C.2
  • 6
    • 0002053804 scopus 로고
    • Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
    • M. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88.
    • (1981) Comm. Math. Phys. , vol.81 , pp. 39-88
    • Jakobson, M.1
  • 7
    • 0039758080 scopus 로고    scopus 로고
    • Computing invariant measures for expanding circle maps
    • R. Keane, M. Murray and L.S. Young, Computing invariant measures for expanding circle maps, Nonlinearity 11 (1998), 27-46.
    • (1998) Nonlinearity , vol.11 , pp. 27-46
    • Keane, R.1    Murray, M.2    Young, L.S.3
  • 8
    • 0001510122 scopus 로고
    • Stochastic stability in some chaotic dynamical systems
    • G. Keller, Stochastic stability in some chaotic dynamical systems, Monatsh. Math. 94 (1982), 313-333.
    • (1982) Monatsh. Math. , vol.94 , pp. 313-333
    • Keller, G.1
  • 10
    • 0031510880 scopus 로고    scopus 로고
    • Computations in dynamical systems via random perturbations
    • Yu. Kifer, Computations in dynamical systems via random perturbations, Discrete and Continuous Dynamical Systems 3 (1997), 457-476.
    • (1997) Discrete and Continuous Dynamical Systems , vol.3 , pp. 457-476
    • Kifer, Yu.1
  • 12
    • 0038455614 scopus 로고    scopus 로고
    • Oral communication to the authors
    • C. Liverani, Oral communication to the authors, (2001).
    • (2001)
    • Liverani, C.1
  • 13
    • 0035346907 scopus 로고    scopus 로고
    • Rigorous numerical investigation of the statistical properties of piecewise expanding maps - A feasibility study
    • _, Rigorous numerical investigation of the statistical properties of piecewise expanding maps - a feasibility study, Nonlinearity 14 (2001), 463-490.
    • (2001) Nonlinearity , vol.14 , pp. 463-490
  • 14
    • 0040341424 scopus 로고
    • Representations of real numbers and their ergodic properties
    • A. Rényi, Representations of real numbers and their ergodic properties, Acta Math.Acad. Sc. Hung. 8. (1957), 477-493.
    • (1957) Acta Math.Acad. Sc. Hung. , vol.8 , pp. 477-493
    • Rényi, A.1
  • 16
    • 0035289437 scopus 로고    scopus 로고
    • Unfolding of chaotic unimodal maps and the parameter dependence of natural measures
    • H. Thunberg, Unfolding of chaotic unimodal maps and the parameter dependence of natural measures, Nonlinearity 14 (2001), 323-337.
    • (2001) Nonlinearity , vol.14 , pp. 323-337
    • Thunberg, H.1
  • 17
    • 85039682400 scopus 로고    scopus 로고
    • Budapest University of Technology and Economics, Scientific Student Competition
    • L.I. Tóth. Digital simulation of chaotic systems, Budapest University of Technology and Economics, Scientific Student Competition (2002).
    • (2002) Digital Simulation of Chaotic Systems
    • Tóth, L.I.1
  • 18
    • 85039675232 scopus 로고    scopus 로고
    • Budapest University of Technology and Economics, Scientific Student Competition
    • R. Tóth, Discrete dynamics of the diadic map, Budapest University of Technology and Economics, Scientific Student Competition (2002).
    • (2002) Discrete Dynamics of the Diadic Map
    • Tóth, R.1
  • 20
    • 0003227072 scopus 로고    scopus 로고
    • Stochastic dynamics of deterministic systems
    • lecture notes
    • M. Viana, Stochastic dynamics of deterministic systems, Col. Bras. de Matematica, lecture notes, 1997.
    • (1997) Col. Bras. de Matematica
    • Viana, M.1
  • 22
    • 0032348050 scopus 로고    scopus 로고
    • Statistical properties of dynamical systems with some hyperbolicity
    • L.S. Young, Statistical properties of dynamical systems with some hyperbolicity, Annals of Mathematics 147 (1998), 585-650.
    • (1998) Annals of Mathematics , vol.147 , pp. 585-650
    • Young, L.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.