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Volumn 149, Issue 3, 2009, Pages 411-460

Bers and Hénon, Painlevé and Schrödinger

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EID: 77953654492     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/00127094-2009-042     Document Type: Article
Times cited : (69)

References (58)
  • 1
    • 77953653913 scopus 로고
    • Travaux de Thurston sur les surfaces: Séminaire Orsay (Orsay, France, 1978)
    • Soc. Math. France, Montrouge
    • Travaux de Thurston sur les surfaces: Séminaire Orsay (Orsay, France, 1978), Astérisque 66/67, Soc. Math. France, Montrouge, 1979.
    • (1979) Astérisque , vol.66-67
  • 2
    • 26844472699 scopus 로고    scopus 로고
    • "Sturmian sequences" in Substitutions in Dynamics, Arithmetics and Combinatorics
    • Springer, Berlin
    • P. ARNOUX, "Sturmian sequences" in Substitutions in Dynamics, Arithmetics and Combinatorics, Lecture Notes in Math. 1794, Springer, Berlin, 2002, 143 - 198.
    • (2002) Lecture Notes in Math , vol.1794 , pp. 143-198
    • Arnoux, P.1
  • 3
    • 22544434033 scopus 로고    scopus 로고
    • Energy and invariant measures for birational surface maps
    • E. BEDFORD and J. DILLER, Energy and invariant measures for birational surface maps, Duke Math. J., 128 (2005), 331 - 368.
    • (2005) Duke Math. J. , vol.128 , pp. 331-368
    • Bedford, E.1    Diller, J.2
  • 5
    • 0000427892 scopus 로고
    • 2, IV: The measure of maximal entropy and laminar currents
    • 2, IV: The measure of maximal entropy and laminar currents, Invent. Math. 112 (1993), 77 - 125.
    • (1993) Invent. Math. , vol.112 , pp. 77-125
    • Bedford, E.1
  • 6
    • 34249928777 scopus 로고
    • 2: Currents, equilibrium measure and hyperbolicity
    • 2: Currents, equilibrium measure and hyperbolicity, Invent. Math. 103 (1991), 69 - 99.
    • (1991) Invent. Math. , vol.103 , pp. 69-99
    • Bedford, E.1    Smillie, J.2
  • 7
    • 84968486309 scopus 로고
    • 2, II: Stable manifolds and recurrence
    • 2, II: Stable manifolds and recurrence, J. Amer. Math. Soc. 4 (1991), 657 - 679.
    • (1991) J. Amer. Math. Soc. , vol.4 , pp. 657-679
    • Bedford, E.1
  • 8
    • 0036328473 scopus 로고    scopus 로고
    • 2, VIII: Quasi-expansion
    • 2, VIII: Quasi-expansion,Amer.J.Math. 124 (2002), 221 - 271.
    • (2002) Amer. J. Math. , vol.124 , pp. 221-271
    • Bedford, E.1
  • 9
    • 15744371234 scopus 로고    scopus 로고
    • Real polynomial diffeomorphisms with maximal entropy: Tangencies
    • E. BEDFORD, Real polynomial diffeomorphisms with maximal entropy: Tangencies, Ann. of Math. (2) 160 (2004), 1 - 26.
    • (2004) Ann. of Math. , vol.2 , Issue.160 , pp. 1-26
    • Bedford, E.1
  • 10
    • 0033245668 scopus 로고    scopus 로고
    • The topology of the relative character varieties of a quadruply-punctured sphere
    • R. L. BENEDETTO and W. M. GOLDMAN, The topology of the relative character varieties of a quadruply-punctured sphere, Experiment. Math. 8 (1999), 85 - 103.
    • (1999) Experiment. Math. , vol.8 , pp. 85-103
    • Benedetto, R.L.1    Goldman, W.M.2
  • 11
    • 0003316111 scopus 로고
    • Braids, Links, and Mapping Class Groups
    • Princeton Univ. Press, Princeton
    • J. S. BIRMAN, Braids, Links, and Mapping Class Groups, Ann. of Math. Stud. 82, Princeton Univ. Press, Princeton, 1974.
    • (1974) Ann. of Math. Stud. , vol.82
    • Birman, J.S.1
  • 13
    • 0012755709 scopus 로고    scopus 로고
    • Markoff triples and quasi-Fuchsian groups
    • B. H. BOWDITCH, Markoff triples and quasi-Fuchsian groups, Proc. London Math. Soc. (3) 77 (1998), 697 - 736.
    • (1998) Proc. London Math. Soc. , vol.3 , Issue.77 , pp. 697-736
    • Bowditch, B.H.1
  • 14
    • 0002371966 scopus 로고
    • "Entropy and the fundamental group" in The Structure of Attractors in Dynamical Systems (Fargo, N.D., 1977)
    • Springer, Berlin
    • R. BOWEN, "Entropy and the fundamental group" in The Structure of Attractors in Dynamical Systems (Fargo, N.D., 1977), Lecture Notes in Math. 668, Springer, Berlin, 1978, 21 - 29.
    • (1978) Lecture Notes in Math , vol.668 , pp. 21-29
    • Bowen, R.1
  • 15
    • 0013501719 scopus 로고
    • The ergodic theory of Axiom A flows
    • R. BOWEN and D. RUELLE, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975), 181 - 202.
    • (1975) Invent. Math. , vol.29 , pp. 181-202
    • Bowen, R.1    Ruelle, D.2
  • 16
    • 67650937821 scopus 로고    scopus 로고
    • The algebraic entropy of the special linear character automorphisms of a free group on two generators
    • R. J. BROWN, The algebraic entropy of the special linear character automorphisms of a free group on two generators,Trans.Amer.Math.Soc.359 (2007), 1445 - 1470.
    • (2007) Trans. Amer. Math. Soc. , vol.359 , pp. 1445-1470
    • Brown, R.J.1
  • 17
    • 0040489280 scopus 로고    scopus 로고
    • Dynamique des automorphismes des surfaces K3
    • S. CANTAT, Dynamique des automorphismes des surfaces K3, Acta Math. 187 (2001), 1 - 57.
    • (2001) Acta Math , vol.187 , pp. 1-57
    • Cantat, S.1
  • 18
    • 0035540496 scopus 로고    scopus 로고
    • Sur la dynamique du groupe d'automorphismes des surfaces K3
    • S. CANTAT, Sur la dynamique du groupe d'automorphismes des surfaces K3, Transform. Groups 6 (2001), 201 - 214.
    • (2001) Transform. Groups , vol.6 , pp. 201-214
    • Cantat, S.1
  • 19
    • 0041351961 scopus 로고    scopus 로고
    • Symétries birationnelles des surfaces feuilletées
    • S. CANTAT and C. FAVRE, Symétries birationnelles des surfaces feuilletées,J.Reine Angew. Math. 561 (2003), 199 - 235.
    • (2003) J. Reine Angew. Math. , vol.561 , pp. 199-235
    • Cantat, S.1    Favre, C.2
  • 20
    • 77953659116 scopus 로고    scopus 로고
    • Holomorphic dynamics, Painlevé VI equation and character varieties
    • preprint, arXiv:0711.1579v2 [math.DS]
    • S. CANTAT and F. LORAY, Holomorphic dynamics, Painlevé VI equation and character varieties, to appear in Ann. Inst. Fourier (Grenoble), preprint, arXiv:0711.1579v2 [math.DS].
    • To appear in Ann. Inst. Fourier (Grenoble)
    • Cantat, S.1    Loray, F.2
  • 21
    • 0000944845 scopus 로고
    • Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation
    • M. CASDAGLI, Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation, Comm. Math. Phys. 107 (1986), 295 - 318.
    • (1986) Comm. Math. Phys. , vol.107 , pp. 295-318
    • Casdagli, M.1
  • 23
    • 0034664283 scopus 로고    scopus 로고
    • Substitution Hamiltonians with bounded trace map orbits
    • D. DAMANIK, Substitution Hamiltonians with bounded trace map orbits,J.Math. Anal. Appl. 249 (2000), 393 - 411.
    • (2000) J. Math. Anal. Appl , vol.249 , pp. 393-411
    • Damanik, D.1
  • 24
    • 41449092902 scopus 로고    scopus 로고
    • "Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: A survey of Kotani theory and its applications" Proc. Sympos. Pure Math. Amer. Math. Soc., Providence
    • D. DAMANIK, "Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: A survey of Kotani theory and its applications" in Spectral Theory and Mathematical Physics, Part 2 (Pasadena, Calif., 2006), Proc. Sympos. Pure Math. 76, Amer. Math. Soc., Providence, 2007, 539 - 563.
    • (2007) Spectral Theory and Mathematical Physics, Part 2 (Pasadena, Calif., 2006) , vol.76 , pp. 539-563
    • Damanik, D.1
  • 26
    • 0035648243 scopus 로고    scopus 로고
    • Dynamics of bimeromorphic maps of surfaces
    • J. DILLER and C. FAVRE, Dynamics of bimeromorphic maps of surfaces,Amer.J. Math. 123 (2001), 1135 - 1169.
    • (2001) Amer. J. Math. , vol.123 , pp. 1135-1169
    • Diller, J.1    Favre, C.2
  • 27
    • 18144384409 scopus 로고    scopus 로고
    • Green currents for holomorphic automorphisms of compact Kähler manifolds
    • T.-C. DINH and N. SIBONY, Green currents for holomorphic automorphisms of compact Kähler manifolds,J.Amer.Math.Soc.18 (2005), 291 - 312.
    • (2005) J. Amer. Math. Soc. , vol.18 , pp. 291-312
    • Dinh, T.-C.1    Sibony, N.2
  • 28
    • 24344460623 scopus 로고    scopus 로고
    • Une borne supérieure pour l'entropie topologique d'une application rationnelle
    • T.-C. DINH, Une borne supérieure pour l'entropie topologique d'une application rationnelle, Ann. of Math. (2) 161 (2005), 1637 - 1644.
    • (2005) Ann. of Math. , vol.2 , Issue.161 , pp. 1637-1644
    • Dinh, T.-C.1
  • 29
    • 0034349066 scopus 로고    scopus 로고
    • Monodromy of certain Painlevé-VI transcendents and reflection groups
    • B. DUBROVIN and M. MAZZOCCO, Monodromy of certain Painlevé-VI transcendents and reflection groups, Invent. Math. 141 (2000), 55 - 147.
    • (2000) Invent. Math. , vol.141 , pp. 55-147
    • Dubrovin, B.1    Mazzocco, M.2
  • 30
    • 33244493567 scopus 로고    scopus 로고
    • Laminar currents and birational dynamics
    • R. DUJARDIN, Laminar currents and birational dynamics, Duke Math. J. 131 (2006), 219 - 247.
    • (2006) Duke Math. J. , vol.131 , pp. 219-247
    • Dujardin, R.1
  • 31
    • 77951172059 scopus 로고
    • Cubic surfaces of Markov type (in Russian)
    • M. H. ÈL'-HUTI, Cubic surfaces of Markov type (in Russian), Mat. Sb. (N.S.) 93 (1974), 331 - 346.
    • (1974) Mat. Sb. (N. S.) , vol.93 , pp. 331-346
    • Èl'-Huti, M.H.1
  • 33
    • 0034178824 scopus 로고    scopus 로고
    • Classification of 2-dimensional contracting rigid germs and Kato surfaces, I
    • C. FAVRE, Classification of 2-dimensional contracting rigid germs and Kato surfaces, I, J. Math. Pures Appl. (9) 79 (2000), 475 - 514.
    • (2000) J. Math. Pures Appl. , vol.9 , Issue.79 , pp. 475-514
    • Favre, C.1
  • 35
    • 0001527326 scopus 로고
    • Topological components of spaces of representations
    • W. M. GOLDMAN, Topological components of spaces of representations, Invent. Math. 93 (1988), 557 - 607.
    • (1988) Invent. Math. , vol.93 , pp. 557-607
    • Goldman, W.M.1
  • 36
    • 0031324962 scopus 로고    scopus 로고
    • Ergodic theory on moduli spaces
    • W. M. GOLDMAN, Ergodic theory on moduli spaces, Ann. of Math. (2) 146 (1997), 475 - 507.
    • (1997) Ann. of Math. , vol.2 , Issue.146 , pp. 475-507
    • Goldman, W.M.1
  • 37
    • 4344601598 scopus 로고    scopus 로고
    • The modular group action on real SL(2)-characters of a one-holed torus
    • W. M. GOLDMAN, The modular group action on real SL(2)-characters of a one-holed torus, Geom. Topol. 7 (2003), 443 - 486.
    • (2003) Geom. Topol. , vol.7 , pp. 443-486
    • Goldman, W.M.1
  • 38
    • 84875130412 scopus 로고    scopus 로고
    • "Mapping class group dynamics on surface group representations" in Problems on Mapping Class Groups and Related Topics
    • Amer. Math. Soc., Providence
    • W. M. GOLDMAN, "Mapping class group dynamics on surface group representations" in Problems on Mapping Class Groups and Related Topics, Proc. Sympos. Pure Math. 74, Amer. Math. Soc., Providence, 2006, 189 - 214.
    • (2006) Proc. Sympos. Pure Math. , vol.74 , pp. 189-214
    • Goldman, W.M.1
  • 39
    • 0000800708 scopus 로고
    • Regularity of the Anosov splitting and of horospheric foliations
    • B. HASSELBLATT, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory Dynam. Systems 14 (1994), 645 - 666.
    • (1994) Ergodic Theory Dynam. Systems , vol.14 , pp. 645-666
    • Hasselblatt, B.1
  • 40
    • 51249166692 scopus 로고
    • Hénon mappings in the complex domain, I: The global topology of dynamical space
    • J. H. HUBBARD and R. W. OBERSTE-VORTH, Hénon mappings in the complex domain, I: The global topology of dynamical space, Inst. Hautes Études Sci. Publ. Math. 79 (1994), 5 - 46.
    • (1994) Inst. Hautes Études Sci. Publ. Math. , vol.79 , pp. 5-46
    • Hubbard, J.H.1    Oberste-Vorth, R.W.2
  • 42
    • 0036764875 scopus 로고    scopus 로고
    • A modular group action on cubic surfaces and the monodromy of the Painlevé VI equation
    • K. IWASAKI, A modular group action on cubic surfaces and the monodromy of the Painlevé VI equation, Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), 131 - 135.
    • (2002) Proc. Japan Acad. Ser. A Math. Sci. , vol.78 , pp. 131-135
    • Iwasaki, K.1
  • 43
    • 38849123788 scopus 로고    scopus 로고
    • "Chaos in the sixth Painlevé equation" in Algebraic, Analytic and Geometric Aspects of Complex Differential Equations and Their Deformations: PainlevéHierarchies
    • 2, Res.Inst. Math. Sci. (RIMS), Kyoto, 2007, 73 - 88.
    • (2007) 2,Res.Inst. Math. Sci. (RIMS), Kyoto , pp. 73-88
    • Iwasaki, K.1    Uehara, T.2
  • 44
    • 34248224932 scopus 로고    scopus 로고
    • An ergodic study of PainlevéVI
    • K. IWASAKI, An ergodic study of PainlevéVI, Math. Ann. 338 (2007), 295 - 345.
    • (2007) Math. Ann. , vol.338 , pp. 295-345
    • Iwasaki, K.1
  • 45
    • 4243445861 scopus 로고
    • Metal-insulator transition and scaling for incommensurate systems
    • M. KOHMOTO, Metal-insulator transition and scaling for incommensurate systems, Phys. Rev. Lett. 51 (1983), 1198 - 1201.
    • (1983) Phys. Rev. Lett. , vol.51 , pp. 1198-1201
    • Kohmoto, M.1
  • 46
    • 0000532658 scopus 로고
    • Localization problem in one dimension: Mapping and escape
    • M. KOHMOTO, L. P. KADANOFF, and C. TANG, Localization problem in one dimension: Mapping and escape, Phys. Rev. Lett. 50 (1983), 1870 - 1872.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 1870-1872
    • Kohmoto, M.1    Kadanoff, L.P.2    Tang, C.3
  • 48
    • 0003336695 scopus 로고    scopus 로고
    • Renormalization and 3-Manifolds Which Fiber over the Circle
    • Princeton Univ. Press, Princeton
    • C. T. MCMULLEN, Renormalization and 3-Manifolds Which Fiber over the Circle, Ann. of Math. Stud. 142, Princeton Univ. Press, Princeton, 1996.
    • (1996) Ann. of Math. Stud. , vol.142
    • Mcmullen, C.T.1
  • 49
    • 0033468108 scopus 로고    scopus 로고
    • The classification of punctured-torus groups
    • Y. N. MINSKY, The classification of punctured-torus groups, Ann. of Math. (2) 149 (1999), 559 - 626.
    • (1999) Ann. of Math. , vol.2 , Issue.149 , pp. 559-626
    • Minsky, Y.N.1
  • 50
    • 77953667805 scopus 로고    scopus 로고
    • End invariants and the classification of hyperbolic 3-manifolds
    • (Cambridge, Mass., 2002), Int. Press, Somerville, Mass
    • Y. N. MINSKY, "End invariants and the classification of hyperbolic 3-manifolds" in Current Developments in Mathematics (Cambridge, Mass., 2002), Int. Press, Somerville, Mass., 2003, 181 - 217.
    • (2003) Current Developments in Mathematics , pp. 181-217
    • Minsky, Y.N.1
  • 51
    • 0001685281 scopus 로고
    • Continuity properties of entropy
    • S. E. NEWHOUSE, Continuity properties of entropy, Ann. of Math. (2) 129 (1989), 215 - 235.
    • (1989) Ann. of Math. , vol.2 , Issue.129 , pp. 215-235
    • Newhouse, S.E.1
  • 52
    • 0003309922 scopus 로고    scopus 로고
    • Dimension Theory in Dynamical Systems: Contemporary Views and Applications
    • Univ. of Chicago Press, Chicago
    • Y. B. PESIN, Dimension Theory in Dynamical Systems: Contemporary Views and Applications, Chicago Lectures in Math., Univ. of Chicago Press, Chicago, 1997.
    • (1997) Chicago Lectures in Math.
    • Pesin, Y.B.1
  • 53
    • 0037214440 scopus 로고    scopus 로고
    • Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps
    • F. PRZYTYCKI, J. RIVERA-LETELIER, and S. SMIRNOV, Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps, Invent. Math. 151 (2003), 29 - 63.
    • (2003) Invent. Math. , vol.151 , pp. 29-63
    • Przytycki, F.1    Rivera-Letelier, J.2    Smirnov, S.3
  • 55
    • 0042334598 scopus 로고    scopus 로고
    • Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension
    • C. SABOT, Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), 275 - 311.
    • (2001) Ann. Inst. H. Poincaré Probab. Statist. , vol.37 , pp. 275-311
    • Sabot, C.1
  • 56
    • 0001858943 scopus 로고    scopus 로고
    • Dynamique et géométrie complexes (Lyon, 1997)
    • N. SIBONY, " Dynamique des applications rationnelles de Pk" in Dynamique et géométrie complexes (Lyon, 1997), Panor. Synthèses 8, Soc. Math. France, Montrouge, 1999, 97 - 185.
    • (1999) Panor. Synthèses 8, Soc. Math. France, Montrouge , pp. 97-185
    • Sibony, N.1
  • 57
    • 0030503430 scopus 로고    scopus 로고
    • Hausdorff dimension of Julia sets of complex Hénon mappings
    • A. VERJOVSKY and H. WU, Hausdorff dimension of Julia sets of complex Hénon mappings, Ergodic Theory Dynam. Systems 16 (1996), 849 - 861.
    • (1996) Ergodic Theory Dynam. Systems , vol.16 , pp. 849-861
    • Verjovsky, A.1    Wu, H.2


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