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Volumn 14, Issue 1, 2001, Pages 25-78

Mating siegel quadratic polynomials

Author keywords

Holomorphic dynamics; Julia set; Mating; Rational map; Siegel disk

Indexed keywords


EID: 0035605968     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-00-00348-9     Document Type: Article
Times cited : (33)

References (62)
  • 1
    • 0001190134 scopus 로고
    • Riemann's mapping theorem for variable metrics
    • L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Annals of Math., 72 (1960) 385-404. MR 22:5813
    • (1960) Annals of Math. , vol.72 , pp. 385-404
    • Ahlfors, L.1    Bers, L.2
  • 2
    • 0346015805 scopus 로고    scopus 로고
    • L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Annals of Math., 72 (1960) 385-404. MR 22:5813
    • MR , vol.22 , pp. 5813
  • 3
    • 84972029136 scopus 로고    scopus 로고
    • Bifurcations of dynamic rays in complex polynomials of degree two
    • P. Atela, Bifurcations of dynamic rays in complex polynomials of degree two, Erg. Th. and Dyn. Sys., 12 (1991) 401-423. MR 94d:58128
    • (1991) Erg. Th. and Dyn. Sys. , vol.12 , pp. 401-423
    • Atela, P.1
  • 4
    • 84972029136 scopus 로고    scopus 로고
    • P. Atela, Bifurcations of dynamic rays in complex polynomials of degree two, Erg. Th. and Dyn. Sys., 12 (1991) 401-423. MR 94d:58128
    • MR , vol.94 D , pp. 58128
  • 5
    • 0000251948 scopus 로고    scopus 로고
    • Ordered orbits of the shift, square roots, and the devil's staircase
    • S. Bullett and P. Sentenac, Ordered orbits of the shift, square roots, and the devil's staircase, Math. Proc. Camb. Phil. Soc., 115 (1994) 451-481. MR 95j:58043
    • (1994) Math. Proc. Camb. Phil. Soc. , vol.115 , pp. 451-481
    • Bullett, S.1    Sentenac, P.2
  • 6
    • 0000251948 scopus 로고    scopus 로고
    • S. Bullett and P. Sentenac, Ordered orbits of the shift, square roots, and the devil's staircase, Math. Proc. Camb. Phil. Soc., 115 (1994) 451-481. MR 95j:58043
    • MR , vol.95 J , pp. 58043
  • 7
    • 0000704409 scopus 로고    scopus 로고
    • Rigidity of critical circle mappings I
    • E. de Faria and W. de Melo, Rigidity of critical circle mappings I, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 4, 339-392. CMP 2000:05
    • (1999) J. Eur. Math. Soc. (JEMS) , vol.1 , Issue.4 , pp. 339-392
    • De Faria, E.1    De Melo, W.2
  • 8
    • 0347907161 scopus 로고    scopus 로고
    • E. de Faria and W. de Melo, Rigidity of critical circle mappings I, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 4, 339-392. CMP 2000:05
    • CMP , vol.2000 , pp. 5
  • 9
    • 0003023968 scopus 로고
    • Algorithms for computing angles in the Mandelbrot set
    • ed. Barnsley and Demko, Academic Press
    • A. Douady, Algorithms for computing angles in the Mandelbrot set, in "Chaotic Dynamics and Fractals," ed. Barnsley and Demko, Academic Press (1986) 155-168. CMP 19:01
    • (1986) Chaotic Dynamics and Fractals , pp. 155-168
    • Douady, A.1
  • 10
    • 0347907177 scopus 로고    scopus 로고
    • A. Douady, Algorithms for computing angles in the Mandelbrot set, in "Chaotic Dynamics and Fractals," ed. Barnsley and Demko, Academic Press (1986) 155-168. CMP 19:01
    • CMP , vol.19 , pp. 1
  • 11
    • 0009068559 scopus 로고
    • Systèmes dynamiques holomorphes
    • A. Douady, Systèmes dynamiques holomorphes, Seminar Bourbaki, Astérisque, 105-106 (1983) 39-63. MR 85h:58090
    • (1983) Seminar Bourbaki, Astérisque , vol.105-106 , pp. 39-63
    • Douady, A.1
  • 12
    • 0346015799 scopus 로고    scopus 로고
    • A. Douady, Systèmes dynamiques holomorphes, Seminar Bourbaki, Astérisque, 105-106 (1983) 39-63. MR 85h:58090
    • MR , vol.85 H , pp. 58090
  • 13
    • 0000195443 scopus 로고
    • Disques de siegel et anneaux de Herman
    • A. Douady, Disques de Siegel et anneaux de Herman, Seminar Bourbaki, Astérisque, 152-153 (1987) 151-172. MR 89g:30049
    • (1987) Seminar Bourbaki, Astérisque , vol.152-153 , pp. 151-172
    • Douady, A.1
  • 14
    • 0346646897 scopus 로고    scopus 로고
    • A. Douady, Disques de Siegel et anneaux de Herman, Seminar Bourbaki, Astérisque, 152-153 (1987) 151-172. MR 89g:30049
    • MR , vol.89 G , pp. 30049
  • 15
    • 0002822579 scopus 로고    scopus 로고
    • Conformally natural extension of homeomorphisms of the circle
    • A. Douady and C. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math., 157 (1986) 23-48. MR 87j:30041
    • (1986) Acta Math. , vol.157 , pp. 23-48
    • Douady, A.1    Earle, C.2
  • 16
    • 0002822579 scopus 로고    scopus 로고
    • A. Douady and C. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math., 157 (1986) 23-48. MR 87j:30041
    • MR , vol.87 J , pp. 30041
  • 17
    • 33846181504 scopus 로고    scopus 로고
    • A proof of Thurston's topological characterization of rational functions
    • A. Douady and J. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math., 171 (1993) 263-297. MR 94j:58143
    • (1993) Acta Math. , vol.171 , pp. 263-297
    • Douady, A.1    Hubbard, J.2
  • 18
    • 33846181504 scopus 로고    scopus 로고
    • A. Douady and J. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math., 171 (1993) 263-297. MR 94j:58143
    • MR , vol.94 J , pp. 58143
  • 20
    • 0032116355 scopus 로고    scopus 로고
    • Chirurgie parabolique
    • P. Haïssinsky, Chirurgie parabolique, C. R. Acad. Sci. Paris, 327 (1998) 195-198. MR 99i:58127
    • (1998) C. R. Acad. Sci. Paris , vol.327 , pp. 195-198
    • Haïssinsky, P.1
  • 21
    • 0032116355 scopus 로고    scopus 로고
    • P. Haïssinsky, Chirurgie parabolique, C. R. Acad. Sci. Paris, 327 (1998) 195-198. MR 99i:58127
    • MR , vol.99 I , pp. 58127
  • 24
    • 84956267205 scopus 로고
    • The dynamics of rational transforms: The topological picture
    • M.Yu. Lyubich, The dynamics of rational transforms: The topological picture, Russian Math. Surveys 41 (1986) 43-117.
    • (1986) Russian Math. Surveys , vol.41 , pp. 43-117
    • Lyubich, M.Yu.1
  • 25
    • 0003028556 scopus 로고
    • Complex dynamics and renormalization
    • C. McMullen, Complex Dynamics and Renormalization, Annals of Math. Studies, vol. 135, 1994. MR 96b:58097
    • (1994) Annals of Math. Studies , vol.135
    • McMullen, C.1
  • 26
    • 0347276917 scopus 로고    scopus 로고
    • C. McMullen, Complex Dynamics and Renormalization, Annals of Math. Studies, vol. 135, 1994. MR 96b:58097
    • MR , vol.96 B , pp. 58097
  • 28
    • 0347276907 scopus 로고    scopus 로고
    • W. de Melo, S. van Strien, One-dimensional dynamics, Springer-Verlag, 1993. MR 95a:58035
    • MR , vol.95 A , pp. 58035
  • 30
    • 4243873888 scopus 로고    scopus 로고
    • J. Milnor, Dynamics in One Complex Variable: Introductory Lectures, Vieweg, 1999 (Available from the American Mathematical Society). CMP 2000:03
    • CMP , vol.2000 , pp. 3
  • 31
    • 84950776875 scopus 로고    scopus 로고
    • Geometry and dynamics of quadratic rational maps
    • J. Milnor, Geometry and dynamics of quadratic rational maps, Experiment. Math., 2 (1993) 37-83. MR 96h:58094
    • (1993) Experiment. Math. , vol.2 , pp. 37-83
    • Milnor, J.1
  • 32
    • 84950776875 scopus 로고    scopus 로고
    • J. Milnor, Geometry and dynamics of quadratic rational maps, Experiment. Math., 2 (1993) 37-83. MR 96h:58094
    • MR , vol.96 H , pp. 58094
  • 33
    • 33749557417 scopus 로고    scopus 로고
    • Periodic orbits, external rays, and the Mandelbrot set: An expository account
    • J. Milnor, Periodic orbits, external rays, and the Mandelbrot set: An expository account, Asterisque 261 (2000). CMP 2000:12
    • (2000) Asterisque , vol.261
    • Milnor, J.1
  • 34
    • 33749557417 scopus 로고    scopus 로고
    • J. Milnor, Periodic orbits, external rays, and the Mandelbrot set: An expository account, Asterisque 261 (2000). CMP 2000:12
    • CMP , vol.2000 , pp. 12
  • 36
    • 0000427353 scopus 로고    scopus 로고
    • Concerning upper semi-continuous collection of continua
    • R.L. Moore, Concerning upper semi-continuous collection of continua, Trans. Amer. Math. Soc., 27 (1925) 416-428. CMP 95:18
    • (1925) Trans. Amer. Math. Soc. , vol.27 , pp. 416-428
    • Moore, R.L.1
  • 37
    • 0000427353 scopus 로고    scopus 로고
    • R.L. Moore, Concerning upper semi-continuous collection of continua, Trans. Amer. Math. Soc., 27 (1925) 416-428. CMP 95:18
    • CMP , vol.95 , pp. 18
  • 38
    • 0000297708 scopus 로고    scopus 로고
    • Local connectivity of some Julia sets containing a circle with an irrational rotation
    • C. Petersen, Local connectivity of some Julia sets containing a circle with an irrational rotation, Acta Math., 177 (1996) 163-224. MR 98h:58164
    • (1996) Acta Math. , vol.177 , pp. 163-224
    • Petersen, C.1
  • 39
    • 0000297708 scopus 로고    scopus 로고
    • C. Petersen, Local connectivity of some Julia sets containing a circle with an irrational rotation, Acta Math., 177 (1996) 163-224. MR 98h:58164
    • MR , vol.98 H , pp. 58164
  • 41
    • 0003075314 scopus 로고    scopus 로고
    • A partial description of parameter space of rational maps of degree two: Part I
    • M. Rees, A partial description of parameter space of rational maps of degree two: part I, Acta Math., 168 (1992) 11-87. MR 93f:58205
    • (1992) Acta Math. , vol.168 , pp. 11-87
    • Rees, M.1
  • 42
    • 0003075314 scopus 로고    scopus 로고
    • M. Rees, A partial description of parameter space of rational maps of degree two: part I, Acta Math., 168 (1992) 11-87. MR 93f:58205
    • MR , vol.93 F , pp. 58205
  • 44
    • 0346015796 scopus 로고    scopus 로고
    • M. Shishikura, On a theorem of M. Rees for matings of polynomials, London Math. Soc. Lecture Note Ser., 274. CMP 2000:14
    • CMP , vol.2000 , pp. 14
  • 45
    • 0000595016 scopus 로고
    • Iteration of analytic functions
    • C. L. Siegel, Iteration of analytic functions, Ann. of Math., 43 (1942) 607-612. MR 4:76C
    • (1942) Ann. of Math. , vol.43 , pp. 607-612
    • Siegel, C.L.1
  • 46
    • 24444433037 scopus 로고    scopus 로고
    • C. L. Siegel, Iteration of analytic functions, Ann. of Math., 43 (1942) 607-612. MR 4:76C
    • MR , vol.4
  • 47
    • 0034349038 scopus 로고    scopus 로고
    • A family of cubic rational maps and matings of cubic polynomials
    • M. Shishikura and L. Tan, A family of cubic rational maps and matings of cubic polynomials, Experiment. Math., 9 (2000) 29-53. CMP 2000:12
    • (2000) Experiment. Math. , vol.9 , pp. 29-53
    • Shishikura, M.1    Tan, L.2
  • 48
    • 0034349038 scopus 로고    scopus 로고
    • M. Shishikura and L. Tan, A family of cubic rational maps and matings of cubic polynomials, Experiment. Math., 9 (2000) 29-53. CMP 2000:12
    • CMP , vol.2000 , pp. 12
  • 49
    • 0001490522 scopus 로고    scopus 로고
    • Rational rotation numbers for maps of the circle
    • G. Swiatek, Rational rotation numbers for maps of the circle, Comm. Math. Phys., 119 (1988) 109-128. MR 90h:58077
    • (1988) Comm. Math. Phys. , vol.119 , pp. 109-128
    • Swiatek, G.1
  • 50
    • 0001490522 scopus 로고    scopus 로고
    • G. Swiatek, Rational rotation numbers for maps of the circle, Comm. Math. Phys., 119 (1988) 109-128. MR 90h:58077
    • MR , vol.90 H , pp. 58077
  • 51
    • 84972048001 scopus 로고    scopus 로고
    • Matings of quadratic polynomials
    • L. Tan, Matings of quadratic polynomials, Erg. Th. and Dyn. Sys. 12 (1992) 589-620. MR 93h:58129
    • (1992) Erg. Th. and Dyn. Sys. , vol.12 , pp. 589-620
    • Tan, L.1
  • 52
    • 84972048001 scopus 로고    scopus 로고
    • L. Tan, Matings of quadratic polynomials, Erg. Th. and Dyn. Sys. 12 (1992) 589-620. MR 93h:58129
    • MR , vol.93 H , pp. 58129
  • 53
    • 0002382991 scopus 로고    scopus 로고
    • Local connectivity of the Julia set for geometrically finite rational maps
    • L. Tan and Y. Yin, Local connectivity of the Julia set for geometrically finite rational maps, Sci. China Ser. A 39 (1996) 39-47. MR 97g:58142
    • (1996) Sci. China Ser. A , vol.39 , pp. 39-47
    • Tan, L.1    Yin, Y.2
  • 54
    • 0002382991 scopus 로고    scopus 로고
    • L. Tan and Y. Yin, Local connectivity of the Julia set for geometrically finite rational maps, Sci. China Ser. A 39 (1996) 39-47. MR 97g:58142
    • MR , vol.97 G , pp. 58142
  • 55
    • 0033483410 scopus 로고    scopus 로고
    • Complex bounds for renormalization of critical circle maps
    • M. Yampolsky, Complex bounds for renormalization of critical circle maps, Erg. Th. and Dyn. Sys., 19 (1999) 227-257. MR 2000d:37053
    • (1999) Erg. Th. and Dyn. Sys. , vol.19 , pp. 227-257
    • Yampolsky, M.1
  • 56
    • 0033483410 scopus 로고    scopus 로고
    • M. Yampolsky, Complex bounds for renormalization of critical circle maps, Erg. Th. and Dyn. Sys., 19 (1999) 227-257. MR 2000d:37053
    • MR , vol.2000 D , pp. 37053
  • 57
    • 0000710552 scopus 로고
    • Il n'y a pas de contre-example de Denjoy analytique
    • J.C. Yoccoz, Il n'y a pas de contre-example de Denjoy analytique, C. R. Acad. Sci. Paris Ser. I Math., 298 (1984) 141-144. MR 85j:58134
    • (1984) C. R. Acad. Sci. Paris Ser. I Math. , vol.298 , pp. 141-144
    • Yoccoz, J.C.1
  • 58
    • 0347907164 scopus 로고    scopus 로고
    • J.C. Yoccoz, Il n'y a pas de contre-example de Denjoy analytique, C. R. Acad. Sci. Paris Ser. I Math., 298 (1984) 141-144. MR 85j:58134
    • MR , vol.85 J , pp. 58134
  • 59
    • 0002419166 scopus 로고
    • Petits diviseurs en dimension 1
    • J.C. Yoccoz, Petits Diviseurs en Dimension 1, Astérisque 231, 1995.
    • (1995) Astérisque , vol.231
    • Yoccoz, J.C.1
  • 60
    • 0346015789 scopus 로고    scopus 로고
    • Biaccessibility in quadratic Julia sets I-II
    • to appear in
    • S. Zakeri, Biaccessibility in quadratic Julia sets I-II, to appear in Erg. Th. and Dyn. Sys.
    • Erg. Th. and Dyn. Sys.
    • Zakeri, S.1
  • 61
    • 0033239027 scopus 로고    scopus 로고
    • Dynamics of cubic Siegel polynomials
    • S. Zakeri, Dynamics of cubic Siegel polynomials, Comm. Math. Phys., 206 (1999) 185-233. CMP 2000:07
    • (1999) Comm. Math. Phys. , vol.206 , pp. 185-233
    • Zakeri, S.1
  • 62
    • 0033239027 scopus 로고    scopus 로고
    • S. Zakeri, Dynamics of cubic Siegel polynomials, Comm. Math. Phys., 206 (1999) 185-233. CMP 2000:07
    • CMP , vol.2000 , pp. 7


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