메뉴 건너뛰기




Volumn 192, Issue 1, 2005, Pages 1-34

Orthonormal expansions of invariant densities for expanding maps

Author keywords

Absolutely continuous invariant measure; Density; Expanding map; Periodic orbits; Transfer operator

Indexed keywords


EID: 11044226315     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aim.2003.09.011     Document Type: Article
Times cited : (13)

References (35)
  • 3
    • 0028445787 scopus 로고
    • The accuracy of numerical conformal mapping methods: A survey of examples and results
    • DeLillo T. The accuracy of numerical conformal mapping methods: a survey of examples and results SIAM J. Numer. Anal. 31 1994 788-812
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 788-812
    • DeLillo, T.1
  • 4
    • 0038739420 scopus 로고    scopus 로고
    • Ulam's scheme revisited: Digital modeling of chaotic attractors via micro-perturbations
    • Domokos G. Szász D. Ulam's scheme revisited: Digital modeling of chaotic attractors via micro-perturbations Discrete Contin. Dyn. Syst. 9 2003 859-876
    • (2003) Discrete Contin. Dyn. Syst. , vol.9 , pp. 859-876
    • Domokos, G.1    Szász, D.2
  • 6
    • 11044233401 scopus 로고
    • Theoretical and numerical analysis of conformal mapping
    • Ph.D. Thesis, MIT, Cambridge, MA
    • M. Dubiner, Theoretical and numerical analysis of conformal mapping, Ph.D. Thesis, MIT, Cambridge, MA, 1981.
    • (1981)
    • Dubiner, M.1
  • 7
    • 44049117207 scopus 로고
    • Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
    • J.-P. Eckmann, D. Ruelle, Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems, Physica D (1992) 185-187.
    • (1992) Physica D , pp. 185-187
    • Eckmann, J.-P.1    Ruelle, D.2
  • 8
    • 0001407441 scopus 로고
    • The zeta functions of Ruelle and Selberg I
    • Fried D. The zeta functions of Ruelle and Selberg I Ann. Sci. Ecole. Norm. Sup. 19 1986 491-517
    • (1986) Ann. Sci. Ecole. Norm. Sup. , vol.19 , pp. 491-517
    • Fried, D.1
  • 9
    • 0032623230 scopus 로고    scopus 로고
    • Using Ulam's method to calculate entropy and other dynamical invariants
    • Froyland G. Using Ulam's method to calculate entropy and other dynamical invariants Nonlinearity 12 1999 79-101
    • (1999) Nonlinearity , vol.12 , pp. 79-101
    • Froyland, G.1
  • 11
    • 84974325811 scopus 로고
    • 1 expanding transformation of the interval without absolutely continuous invariant probability measure
    • 1 expanding transformation of the interval without absolutely continuous invariant probability measure Ergodic Theory Dynamical Systems 9 1989 101-113
    • (1989) Ergodic Theory Dynamical Systems , vol.9 , pp. 101-113
    • Góra, P.1    Schmitt, B.2
  • 14
    • 11044226710 scopus 로고
    • Computation of conformal maps by modified Schwarz-Christoffel transformations
    • Ph.D. Thesis, MIT, Cambridge, MA
    • L.H. Howell, Computation of conformal maps by modified Schwarz-Christoffel transformations, Ph.D. Thesis, MIT, Cambridge, MA, 1990.
    • (1990)
    • Howell, L.H.1
  • 15
    • 0041051009 scopus 로고    scopus 로고
    • Estimating invariant measures and Lyapunov exponents
    • Hunt B.R. Estimating invariant measures and Lyapunov exponents Ergodic Theory Dynamical Systems 16 1996 735-749
    • (1996) Ergodic Theory Dynamical Systems , vol.16 , pp. 735-749
    • Hunt, B.R.1
  • 16
    • 0034348970 scopus 로고    scopus 로고
    • Computing invariant densities and metric entropy
    • Jenkinson O. Pollicott M. Computing invariant densities and metric entropy Comm. Math. Phys. 211 2000 687-703
    • (2000) Comm. Math. Phys. , vol.211 , pp. 687-703
    • Jenkinson, O.1    Pollicott, M.2
  • 18
    • 0039758080 scopus 로고    scopus 로고
    • Computing invariant measures for expanding circle maps
    • Keane M. Murray R. Young L.-S. Computing invariant measures for expanding circle maps Nonlinearity 11 1998 27-46
    • (1998) Nonlinearity , vol.11 , pp. 27-46
    • Keane, M.1    Murray, R.2    Young, L.-S.3
  • 19
    • 84966227493 scopus 로고
    • On the existence of invariant measures for piecewise monotonic transformations
    • Lasota A. Yorke J.A. On the existence of invariant measures for piecewise monotonic transformations Trans. Amer. Math. Soc. 186 1973 481-488
    • (1973) Trans. Amer. Math. Soc. , vol.186 , pp. 481-488
    • Lasota, A.1    Yorke, J.A.2
  • 21
    • 0035346907 scopus 로고    scopus 로고
    • Rigorous numerical investigation of the statistical properties of piecewise expanding maps - A feasibility study
    • Liverani C. 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
    • Liverani, C.1
  • 22
    • 0000475519 scopus 로고
    • On composition operators on Banach spaces of holomorphic functions
    • Mayer D. On composition operators on Banach spaces of holomorphic functions J. Funct. Anal. 35 1980 191-206
    • (1980) J. Funct. Anal. , vol.35 , pp. 191-206
    • Mayer, D.1
  • 23
    • 0002562682 scopus 로고
    • Continued fractions and related transformations
    • T. Bedford, M. Keane, C. Series (Eds.), Trieste, OUP, Oxford, 1989
    • D. Mayer, Continued fractions and related transformations, in: T. Bedford, M. Keane, C. Series (Eds.), Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Trieste, 1989, OUP, Oxford, 1991, pp. 175-222.
    • (1991) Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces , pp. 175-222
    • Mayer, D.1
  • 24
    • 0003460576 scopus 로고    scopus 로고
    • Discrete approximation of invariant densities
    • Ph.D. Thesis, Cambridge
    • R. Murray, Discrete approximation of invariant densities, Ph.D. Thesis, Cambridge, 1997.
    • (1997)
    • Murray, R.1
  • 25
    • 0000271607 scopus 로고
    • Zeta functions and the periodic orbit structure of hyperbolic dynamics
    • Paris: Soc. Math. France
    • Parry W. Pollicott M. Zeta functions and the periodic orbit structure of hyperbolic dynamics in: Astérisque Vol. 187-188 1990 Soc. Math. France Paris
    • (1990) Astérisque , vol.187-188
    • Parry, W.1    Pollicott, M.2
  • 26
    • 84961291543 scopus 로고
    • Lyapunov characteristic exponents and smooth ergodic theory
    • Pesin J.B. Lyapunov characteristic exponents and smooth ergodic theory Russian Math. Surveys 32 1977 55-114
    • (1977) Russian Math. Surveys , vol.32 , pp. 55-114
    • Pesin, J.B.1
  • 27
    • 0001085798 scopus 로고
    • Zeta functions for expanding maps and Anosov flows
    • Ruelle D. Zeta functions for expanding maps and Anosov flows Invent. Math. 34 1976 231-242
    • (1976) Invent. Math. , vol.34 , pp. 231-242
    • Ruelle, D.1
  • 29
    • 0141774921 scopus 로고
    • The thermodynamic formalism for expanding maps
    • Ruelle D. The thermodynamic formalism for expanding maps Comm. Math. Phys. 125 1989 239-262
    • (1989) Comm. Math. Phys. , vol.125 , pp. 239-262
    • Ruelle, D.1
  • 30
    • 51649157555 scopus 로고
    • An extension of the theory of Fredholm determinants
    • Ruelle D. An extension of the theory of Fredholm determinants Publ. Math. (IHES) 72 1990 175-193
    • (1990) Publ. Math. (IHES) , vol.72 , pp. 175-193
    • Ruelle, D.1
  • 31
    • 0001130130 scopus 로고
    • Endomorphisms of compact differentiable manifolds
    • Shub M. Endomorphisms of compact differentiable manifolds Amer. J. Math. 91 1969 175-199
    • (1969) Amer. J. Math. , vol.91 , pp. 175-199
    • Shub, M.1
  • 32
    • 0003335754 scopus 로고
    • Trace Ideals and their Applications
    • Cambridge: Cambridge University Press
    • Simon B. Trace Ideals and their Applications LMS Lecture Note Series Vol. 35 1979 Cambridge University Press Cambridge
    • (1979) LMS Lecture Note Series , vol.35
    • Simon, B.1
  • 33
    • 0004073954 scopus 로고
    • 4th Edition, AMS Colloquium Publications, Providence, RI
    • G. Szegö, Orthogonal Polynomials, Vol. 23, 4th Edition, AMS Colloquium Publications, Providence, RI, 1975.
    • (1975) Orthogonal Polynomials , vol.23
    • Szegö, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.