메뉴 건너뛰기




Volumn 173, Issue 2, 2008, Pages 365-425

Thermodynamics, dimension and the Weil-Petersson metric

Author keywords

[No Author keywords available]

Indexed keywords


EID: 45849092922     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-008-0121-2     Document Type: Article
Times cited : (95)

References (47)
  • 1
    • 0032675210 scopus 로고    scopus 로고
    • Multifractal dimensions and thermodynamical description of nearly-circular Julia sets
    • Abenda, S., Moussa, P., Osbaldestin, A.H.: Multifractal dimensions and thermodynamical description of nearly-circular Julia sets. Nonlinearity 12, 19-40 (1999)
    • (1999) Nonlinearity , vol.12 , pp. 19-40
    • Abenda, S.1    Moussa, P.2    Osbaldestin, A.H.3
  • 2
    • 45849153917 scopus 로고    scopus 로고
    • Uniformization and moduli (1960)
    • Am. Math. Soc.
    • Bers, L.: Uniformization and moduli (1960). In: Selected Works of Lipman Bers, Part 1, pp. 299-308. Am. Math. Soc. (1998)
    • (1998) Selected Works of Lipman Bers , Issue.PART 1 , pp. 299-308
    • Bers, L.1
  • 3
    • 0001652473 scopus 로고
    • The geometry of Teichmüller space via geodesic currents
    • Bonahon, F.: The geometry of Teichmüller space via geodesic currents. Invent. Math. 92, 139-162 (1988)
    • (1988) Invent. Math. , vol.92 , pp. 139-162
    • Bonahon, F.1
  • 5
    • 33750471636 scopus 로고    scopus 로고
    • Patterson-Sullivan measures and quasi-conformal deformations
    • Bridgeman, M., Taylor, E.C.: Patterson-Sullivan measures and quasi-conformal deformations. Commun. Anal. Geom. 13, 561-589 (2005)
    • (2005) Commun. Anal. Geom. , vol.13 , pp. 561-589
    • Bridgeman, M.1    Taylor, E.C.2
  • 6
    • 44449147396 scopus 로고    scopus 로고
    • An extension of the Weil-Petersson metric to the quasi-Fuchsian space
    • (to appear)
    • Bridgeman, M., Taylor, E.C.: An extension of the Weil-Petersson metric to the quasi-Fuchsian space. Math. Ann. (to appear)
    • Math. Ann.
    • Bridgeman, M.1    Taylor, E.C.2
  • 7
    • 84963057263 scopus 로고
    • Intersection, the Manhattan curve, and Patterson-Sullivan theory in rank 2
    • Burger, M.: Intersection, the Manhattan curve, and Patterson-Sullivan theory in rank 2. Int. Math. Res. Not. 7, 217-225 (1993)
    • (1993) Int. Math. Res. Not. , vol.7 , pp. 217-225
    • Burger, M.1
  • 8
    • 0038469575 scopus 로고    scopus 로고
    • Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity
    • DeMarco, L.: Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity. Math. Ann. 326, 43-73 (2003)
    • (2003) Math. Ann. , vol.326 , pp. 43-73
    • Demarco, L.1
  • 9
    • 0000454046 scopus 로고
    • Approximation by Brownian motion for Gibbs measures and flows under a function
    • Denker, M., Philipp, W.: Approximation by Brownian motion for Gibbs measures and flows under a function. Ergodic Theory Dyn. Syst. 4, 541-552 (1984)
    • (1984) Ergodic Theory Dyn. Syst. , vol.4 , pp. 541-552
    • Denker, M.1    Philipp, W.2
  • 10
    • 84973997991 scopus 로고
    • Mixing, counting and equidistribution in Lie groups
    • Eskin, A., McMullen, C.: Mixing, counting and equidistribution in Lie groups. Duke Math. J. 71, 181-209 (1993)
    • (1993) Duke Math. J. , vol.71 , pp. 181-209
    • Eskin, A.1    McMullen, C.2
  • 11
    • 30144445377 scopus 로고    scopus 로고
    • Harmonic currents of finite energy and laminations
    • Fornaess, J.E., Sibony, N.: Harmonic currents of finite energy and laminations. Geom. Funct. Anal. 15, 962-1003 (2005)
    • (2005) Geom. Funct. Anal. , vol.15 , pp. 962-1003
    • Fornaess, J.E.1    Sibony, N.2
  • 12
    • 0000454356 scopus 로고
    • Symmetric structures on a closed curve
    • Gardiner, F.P., Sullivan, D.P.: Symmetric structures on a closed curve. Am. J. Math. 114, 683-736 (1992)
    • (1992) Am. J. Math. , vol.114 , pp. 683-736
    • Gardiner, F.P.1    Sullivan, D.P.2
  • 13
    • 0010756697 scopus 로고
    • Lacunary series as quadratic differentials in conformal dynamics
    • The Mathematical Legacy of Wilhelm Magnus: Groups, Geometry and Special Functions. Am. Math. Soc.
    • Gardiner, F.P., Sullivan, D.P.: Lacunary series as quadratic differentials in conformal dynamics. In: The Mathematical Legacy of Wilhelm Magnus: Groups, Geometry and Special Functions. Contemp. Math., vol. 169, pp. 307-330. Am. Math. Soc. (1994)
    • (1994) Contemp. Math. , vol.169 , pp. 307-330
    • Gardiner, F.P.1    Sullivan, D.P.2
  • 14
    • 0000721332 scopus 로고
    • Foliations, the ergodic theorem and Brownian motion
    • Garnett, L.: Foliations, the ergodic theorem and Brownian motion. J. Funct. Anal. 51, 285-311 (1983)
    • (1983) J. Funct. Anal. , vol.51 , pp. 285-311
    • Garnett, L.1
  • 16
    • 0031227425 scopus 로고    scopus 로고
    • Laminations in holomorphic dynamics
    • Lyubich, M., Minsky, Y.: Laminations in holomorphic dynamics. J. Differ. Geom. 47, 17-94 (1997)
    • (1997) J. Differ. Geom. , vol.47 , pp. 17-94
    • Lyubich, M.1    Minsky, Y.2
  • 17
    • 84959830189 scopus 로고
    • On the distortion of boundary sets under conformal mappings
    • Makarov, N.G.: On the distortion of boundary sets under conformal mappings. Proc. Lond. Math. Soc., III. Ser. 51, 369-384 (1985)
    • (1985) Proc. Lond. Math. Soc., III. Ser. , vol.51 , pp. 369-384
    • Makarov, N.G.1
  • 18
    • 0002841256 scopus 로고
    • The Hausdorff dimension of invariant probabilities of rational maps
    • Dynamical Systems, Valparaiso 1986. Springer
    • Mañé, R.: The Hausdorff dimension of invariant probabilities of rational maps. In: Dynamical Systems, Valparaiso 1986. Lect. Notes Math., vol. 1331, pp. 86-117. Springer (1988)
    • (1988) Lect. Notes Math. , vol.1331 , pp. 86-117
    • Mañé, R.1
  • 19
    • 0010176177 scopus 로고
    • The dimension of the maximal measure for a polynomial map
    • Manning, A.: The dimension of the maximal measure for a polynomial map. Ann. Math. 119, 425-430 (1984)
    • (1984) Ann. Math. , vol.119 , pp. 425-430
    • Manning, A.1
  • 20
    • 0011452763 scopus 로고
    • On finite Blaschke products whose restrictions to the unit circle are exact endomorphisms
    • Martin, N.F.G.: On finite Blaschke products whose restrictions to the unit circle are exact endomorphisms. Bull. Lond. Math. Soc. 15, 343-348 (1983)
    • (1983) Bull. Lond. Math. Soc. , vol.15 , pp. 343-348
    • Martin, N.F.G.1
  • 22
    • 0003028556 scopus 로고
    • Complex Dynamics and Renormalization
    • Princeton University Press
    • McMullen, C.: Complex Dynamics and Renormalization. Ann. Math. Stud., vol. 135. Princeton University Press (1994)
    • (1994) Ann. Math. Stud. , vol.135
    • McMullen, C.1
  • 23
    • 0007138616 scopus 로고
    • Rational maps and Teichmüller space
    • Havin, V.P., Nikolskii, N. K. (eds.) Linear and Complex Analysis Problem Book. Springer
    • McMullen, C.: Rational maps and Teichmüller space. In: Havin, V.P., Nikolskii, N. K. (eds.) Linear and Complex Analysis Problem Book. Lect. Notes Math., vol. 1574, pp. 430-433. Springer (1994)
    • (1994) Lect. Notes Math. , vol.1574 , pp. 430-433
    • McMullen, C.1
  • 24
    • 0001218332 scopus 로고
    • The classification of conformal dynamical systems
    • International Press (1995)
    • McMullen, C.: The classification of conformal dynamical systems. In: Current Developments in Mathematics, 1995, pp. 323-360. International Press (1995)
    • (1995) Current Developments in Mathematics , pp. 323-360
    • McMullen, C.1
  • 25
    • 0003336695 scopus 로고    scopus 로고
    • Renormalization and 3-Manifolds which Fiber over the Circle
    • Princeton University Press
    • McMullen, C.: Renormalization and 3-Manifolds which Fiber over the Circle. Ann. Math. Stud., vol. 142. Princeton University Press (1996)
    • (1996) Ann. Math. Stud. , vol.142
    • McMullen, C.1
  • 26
    • 0032385282 scopus 로고    scopus 로고
    • Complex earthquakes and Teichmüller theory
    • McMullen, C.: Complex earthquakes and Teichmüller theory. J. Am. Math. Soc. 11, 283-320 (1998)
    • (1998) J. Am. Math. Soc. , vol.11 , pp. 283-320
    • McMullen, C.1
  • 27
    • 0001579032 scopus 로고    scopus 로고
    • Hausdorff dimension and conformal dynamics III: Computation of dimension
    • McMullen, C.: Hausdorff dimension and conformal dynamics III: Computation of dimension. Am. J. Math. 120, 691-721 (1998)
    • (1998) Am. J. Math. , vol.120 , pp. 691-721
    • McMullen, C.1
  • 28
    • 14644396555 scopus 로고    scopus 로고
    • Statistical limit theorems for suspension flows
    • Melbourne, I. Török, A.: Statistical limit theorems for suspension flows. Isr. J. Math. 144, 191-209 (2004)
    • (2004) Isr. J. Math. , vol.144 , pp. 191-209
    • Melbourne Török, I.A.1
  • 30
    • 3142676437 scopus 로고    scopus 로고
    • Pasting together Julia sets: A worked out example of mating
    • Milnor, J.: Pasting together Julia sets: a worked out example of mating. Exp. Math. 13, 55-92 (2004)
    • (2004) Exp. Math. , vol.13 , pp. 55-92
    • Milnor, J.1
  • 31
    • 0000271607 scopus 로고
    • Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics
    • Parry, W., Pollicott, M.: Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics. Astérisque, vol. 187-188 (1990)
    • (1990) Astérisque , vol.187-188
    • Parry, W.1    Pollicott, M.2
  • 32
    • 0033409513 scopus 로고    scopus 로고
    • On the mixing of Axiom a attracting flows and a conjecture of Ruelle
    • Pollicott, M.: On the mixing of Axiom A attracting flows and a conjecture of Ruelle. Ergodic Theory Dyn. Syst. 19, 535-548 (1999)
    • (1999) Ergodic Theory Dyn. Syst. , vol.19 , pp. 535-548
    • Pollicott, M.1
  • 35
    • 84926802106 scopus 로고
    • Repellers for real analytic maps
    • Ruelle, D.: Repellers for real analytic maps. Ergodic Theory Dyn. Syst. 2, 99-107 (1982)
    • (1982) Ergodic Theory Dyn. Syst. , vol.2 , pp. 99-107
    • Ruelle, D.1
  • 36
    • 0013554411 scopus 로고
    • Flots qui ne mélangent pas exponentiellement
    • Ruelle, D.: Flots qui ne mélangent pas exponentiellement. C. R. Acad. Sci., Paris, Sér. I, Math. 296, 191-193 (1983)
    • (1983) C. R. Acad. Sci., Paris, Sér. I, Math. , vol.296 , pp. 191-193
    • Ruelle, D.1
  • 37
    • 0002739011 scopus 로고
    • On the estimation of Fourier coefficients of modular forms
    • Am. Math. Soc.
    • Selberg, A.: On the estimation of Fourier coefficients of modular forms. In: Proc. Sympos. Pure Math., Vol. VIII, pp. 1-15. Am. Math. Soc. (1965)
    • (1965) Proc. Sympos. Pure Math. , vol.8 , pp. 1-15
    • Selberg, A.1
  • 38
    • 0009317430 scopus 로고
    • The central limit theorem for geodesic flows on manifolds of constant negative curvature
    • Sinai, Y.G.: The central limit theorem for geodesic flows on manifolds of constant negative curvature. Sov. Math. Dokl. 1, 983-987 (1960)
    • (1960) Sov. Math. Dokl. , vol.1 , pp. 983-987
    • Sinai, Y.G.1
  • 39
    • 0000696637 scopus 로고
    • Quasiconformal homeomorphisms and dynamics II: Structural stability implies hyperbolicity for Kleinian groups
    • Sullivan, D.: Quasiconformal homeomorphisms and dynamics II: Structural stability implies hyperbolicity for Kleinian groups. Acta Math. 155, 243-260 (1985)
    • (1985) Acta Math. , vol.155 , pp. 243-260
    • Sullivan, D.1
  • 40
    • 0002958690 scopus 로고
    • Quasiconformal homeomorphisms in dynamics, topology and geometry
    • Am. Math. Soc.
    • Sullivan, D.: Quasiconformal homeomorphisms in dynamics, topology and geometry. In: Proceedings of the International Conference of Mathematicians, pp. 1216-1228. Am. Math. Soc. (1986)
    • (1986) Proceedings of the International Conference of Mathematicians , pp. 1216-1228
    • Sullivan, D.1
  • 41
    • 0000419015 scopus 로고
    • Bounds, quadratic differentials and renormalization conjectures
    • Browder, F. (ed.) August 8-12 Am. Math. Soc.
    • Sullivan, D.: Bounds, quadratic differentials and renormalization conjectures. In: Browder, F. (ed.) Mathematics into the Twenty-first Century: 1988 Centennial Symposium, August 8-12, pp. 417-466. Am. Math. Soc. (1992)
    • (1992) Mathematics into the Twenty-first Century: 1988 Centennial Symposium , pp. 417-466
    • Sullivan, D.1
  • 42
    • 0002016909 scopus 로고
    • Linking the universalities of Milnor-Thurston, Feigenbaum and Ahlfors-Bers
    • Goldberg, L.R., Phillips, A.V. (eds.) Publish or Perish, Inc.
    • Sullivan, D.: Linking the universalities of Milnor-Thurston, Feigenbaum and Ahlfors-Bers. In: Goldberg, L.R., Phillips, A.V. (eds.) Topological Methods in Modern Mathematics, pp. 543-564. Publish or Perish, Inc. (1993)
    • (1993) Topological Methods in Modern Mathematics , pp. 543-564
    • Sullivan, D.1
  • 43
    • 84972048001 scopus 로고
    • Matings of quadratic polynomials
    • Tan, L.: Matings of quadratic polynomials. Ergodic Theory Dyn. Syst. 12, 589-620 (1992)
    • (1992) Ergodic Theory Dyn. Syst. , vol.12 , pp. 589-620
    • Tan, L.1
  • 44
    • 45849104659 scopus 로고
    • On the moduli of Riemann surfaces
    • Springer
    • Weil, A.: [1958b] On the moduli of Riemann surfaces. In: Oeuvres Scient., vol. II, pp. 381-389. Springer (1980)
    • (1958) Oeuvres Scient. , vol.2 , pp. 381-389
    • Weil, A.1
  • 45
    • 84966232592 scopus 로고
    • An asymptotic formula for the Taylor coefficients of automorphic forms
    • Wolpert, S.: An asymptotic formula for the Taylor coefficients of automorphic forms. Proc. Am. Math. Soc. 78, 485-491 (1980)
    • (1980) Proc. Am. Math. Soc. , vol.78 , pp. 485-491
    • Wolpert, S.1
  • 46
    • 84972533526 scopus 로고
    • Thurston's Riemannian metric for Teichmüller space
    • Wolpert, S.: Thurston's Riemannian metric for Teichmüller space. J. Differ. Geom. 23, 143-174 (1986)
    • (1986) J. Differ. Geom. , vol.23 , pp. 143-174
    • Wolpert, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.