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Dynamics of hyperbolic meromorphic functions
1. | Department of Mathematical Sciences, Tsinghua University, Beijing, China |
References:
[1] |
I. N. Baker and P. Dominguez, Boundaries of unbounded Fatou components of entire functions,, Ann. Acad. Sci. Fenn., 24 (1999), 437.
|
[2] |
K. Baranski, Hausdorff dimension and measures on Julia sets of some meromorphic functions,, Fund. Math., 147 (1995), 239.
|
[3] |
W. Bergweiler and A. Eremenko, Meromorphic functions with two completely invariant domains, in Transcendental Dynamics and Complex Analysis,, edited by P. J. Rippon & G. M. Stallard, 348 (2008), 74.
doi: 10.1017/CBO9780511735233.005. |
[4] |
W. Bergweiler, M. Haruta, H. Kriete. H. G. Meier and N. Terglane, On the limit functions of iterates in wandering domains,, Ann. Acad. Sci. Fenn., 18 (1993), 369.
|
[5] |
W. Bergweiler, P. J. Rippon and G. M. Stallard, Dynamics of meromorphic functions with direct or logarithmic singularities,, Proc. London Math. Soc., 97 (2008), 368.
doi: 10.1112/plms/pdn007. |
[6] |
R. L. Devaney and L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative,, Ann. Scient. Éc. Norm. Sup., 22 (1989), 55.
|
[7] |
P. Dominguez, Dynamics of transcendental meromorphic functions,, Ann. Acad. Sci. Fenn., 23 (1998), 225.
|
[8] |
K. Falconer, Fractal Geometry,, John Wiley & Sons, (1999).
doi: 10.1002/0470013850. |
[9] |
W. K. Hayman, On Iversen's Theorem for meromorphic functions with few poles,, Acta Mathematica, 141 (1978), 115.
doi: 10.1007/BF02545745. |
[10] |
F. Iversen, Recherches sur les Fonctions Inverses des Fonctons Méromorphes,, Thése de Helsingfors, (1914). Google Scholar |
[11] |
J. Kotus and M. Urbanski, Conformal, geometric and invariant measures for transcendental expanding functions,, Math. Ann., 324 (2002), 619.
doi: 10.1007/s00208-002-0356-y. |
[12] |
J. Kotus and M. Urbanski, Hausdorff dimension of radial and escaping points for transcendental meromorphic functions,, Illinois J. Math., 52 (2008), 1035.
|
[13] |
V. Mayer and M. Urbański, Thermodynamical formalism and multifractal analysis for meromorphic functions of finite order,, Memoirs of AMS, 203 (2010).
doi: 10.1090/S0065-9266-09-00577-8. |
[14] |
C. McMullen, Area and Hausdorff dimension of Julia sets of entire functions,, Trans. Amer. Math. Soc., 300 (1987), 329.
doi: 10.1090/S0002-9947-1987-0871679-3. |
[15] |
C. McMullen, In holomorphic functions and moduli I,, Springer-Verlag, 10 (1988), 31.
doi: 10.1007/978-1-4613-9602-4_3. |
[16] |
J. K. Moser, Stable And Random Motions In Dynamical Systems,, Princeton: Princeton University Press, (1973).
|
[17] |
T. W. Ng, J. H. Zheng and K. Choi, Residual Julia sets of meromorphic functions,, Math. Proc. Cambridge Phil. Soc., 141 (2006), 113.
doi: 10.1017/S0305004106009388. |
[18] |
K. Pilgrim and L. Tan, Rational maps with disconnected Julia set,, Géométrie complexe et systèmes dynamiques (Orsay, 261 (2000), 349.
|
[19] |
P. J. Rippon and G. M. Stallard, Iteration of a class of hyperbolic meromorphic functions,, Proc. Amer. Math. Soc., 127 (1999), 3251.
doi: 10.1090/S0002-9939-99-04942-4. |
[20] |
D. Ruelle, Repellers for real analytic maps,, Ergodic Th. Dyn. Sys., 2 (1982), 99.
doi: 10.1017/S0143385700009603. |
[21] |
G. M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions,, J. London Math. soc., 49 (1994), 281.
doi: 10.1112/jlms/49.2.281. |
[22] |
G. M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions II,, J. London Math. soc., 60 (1999), 847.
doi: 10.1112/S0024610799008029. |
[23] |
G. M. Stallard, Dimension of Julia sets of hyperbolic meromorphic functions,, Math. Proc. Camb. Phil. Soc., 127 (1999), 271.
doi: 10.1017/S0305004199003813. |
[24] |
G. M. Stallard, The Hausdorff dimension of Julia sets of hyperbolic meromorphic functions,, Ergodic Theory Dynam. Systems, 20 (2000), 895.
doi: 10.1017/S0143385700000481. |
[25] |
G. M. Stallard, Meromorphic functions whose Julia sets contain a free Jordan arc,, Ann. Acad. Sci. Fenn., 18 (1993), 273.
|
[26] |
N. Steinmetz, Rational Iterations,, Berlin: Walter de Gruyter, (1993).
doi: 10.1515/9783110889314. |
[27] |
D. Sullivan, Conformal dynamical systems: In Geometric dynamics,, Lecture Notes in Math., 1007 (1983), 725.
doi: 10.1007/BFb0061443. |
[28] |
O. Teichmüller, Eine Umkehrung des zweiten Hauptsatzes der Wertverteilungstheorie,, Deutsche Math., 2 (1937), 96. Google Scholar |
[29] |
L. A. Ter-Israelyan, Meromorphic functions of zero order with non-asymptotic deficient values,, Math. Zam., 13 (1973), 195.
|
[30] |
P. Walters, Invariant measures and equilibrium states for some mappings which expand distances,, Trans. Amer. Math. Soc., 236 (1978), 121.
doi: 10.1090/S0002-9947-1978-0466493-1. |
[31] |
M. Urbanski and A. Zdunik, The finer geometry and dynamics of exponential family,, Michingan Math. J., 51 (2003), 227.
doi: 10.1307/mmj/1060013195. |
[32] |
M. Urbanski and A. Zdunik, Real analyticity of Hausdorff dimension of finer Julia sets of exponential family,, Ergodic Th. and Dynam. Sys., 24 (2004), 279.
doi: 10.1017/S0143385703000208. |
[33] |
J. H. Zheng, Singularties and limit functions in iteration of meromorphic functions,, J. London Math. Soc., 67 (2003), 195.
doi: 10.1112/S0024610702003800. |
[34] |
J. H. Zheng, On transcendental meromorphic functions which are geometrically finite,, J. Austral. Math. Soc., 72 (2002), 93.
doi: 10.1017/S144678870000361X. |
[35] |
J. H. Zheng, Dynamics Of Meromorphic Functions, Monograph of Tsinghua University,, Tsinghua University Press, (2006). Google Scholar |
show all references
References:
[1] |
I. N. Baker and P. Dominguez, Boundaries of unbounded Fatou components of entire functions,, Ann. Acad. Sci. Fenn., 24 (1999), 437.
|
[2] |
K. Baranski, Hausdorff dimension and measures on Julia sets of some meromorphic functions,, Fund. Math., 147 (1995), 239.
|
[3] |
W. Bergweiler and A. Eremenko, Meromorphic functions with two completely invariant domains, in Transcendental Dynamics and Complex Analysis,, edited by P. J. Rippon & G. M. Stallard, 348 (2008), 74.
doi: 10.1017/CBO9780511735233.005. |
[4] |
W. Bergweiler, M. Haruta, H. Kriete. H. G. Meier and N. Terglane, On the limit functions of iterates in wandering domains,, Ann. Acad. Sci. Fenn., 18 (1993), 369.
|
[5] |
W. Bergweiler, P. J. Rippon and G. M. Stallard, Dynamics of meromorphic functions with direct or logarithmic singularities,, Proc. London Math. Soc., 97 (2008), 368.
doi: 10.1112/plms/pdn007. |
[6] |
R. L. Devaney and L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative,, Ann. Scient. Éc. Norm. Sup., 22 (1989), 55.
|
[7] |
P. Dominguez, Dynamics of transcendental meromorphic functions,, Ann. Acad. Sci. Fenn., 23 (1998), 225.
|
[8] |
K. Falconer, Fractal Geometry,, John Wiley & Sons, (1999).
doi: 10.1002/0470013850. |
[9] |
W. K. Hayman, On Iversen's Theorem for meromorphic functions with few poles,, Acta Mathematica, 141 (1978), 115.
doi: 10.1007/BF02545745. |
[10] |
F. Iversen, Recherches sur les Fonctions Inverses des Fonctons Méromorphes,, Thése de Helsingfors, (1914). Google Scholar |
[11] |
J. Kotus and M. Urbanski, Conformal, geometric and invariant measures for transcendental expanding functions,, Math. Ann., 324 (2002), 619.
doi: 10.1007/s00208-002-0356-y. |
[12] |
J. Kotus and M. Urbanski, Hausdorff dimension of radial and escaping points for transcendental meromorphic functions,, Illinois J. Math., 52 (2008), 1035.
|
[13] |
V. Mayer and M. Urbański, Thermodynamical formalism and multifractal analysis for meromorphic functions of finite order,, Memoirs of AMS, 203 (2010).
doi: 10.1090/S0065-9266-09-00577-8. |
[14] |
C. McMullen, Area and Hausdorff dimension of Julia sets of entire functions,, Trans. Amer. Math. Soc., 300 (1987), 329.
doi: 10.1090/S0002-9947-1987-0871679-3. |
[15] |
C. McMullen, In holomorphic functions and moduli I,, Springer-Verlag, 10 (1988), 31.
doi: 10.1007/978-1-4613-9602-4_3. |
[16] |
J. K. Moser, Stable And Random Motions In Dynamical Systems,, Princeton: Princeton University Press, (1973).
|
[17] |
T. W. Ng, J. H. Zheng and K. Choi, Residual Julia sets of meromorphic functions,, Math. Proc. Cambridge Phil. Soc., 141 (2006), 113.
doi: 10.1017/S0305004106009388. |
[18] |
K. Pilgrim and L. Tan, Rational maps with disconnected Julia set,, Géométrie complexe et systèmes dynamiques (Orsay, 261 (2000), 349.
|
[19] |
P. J. Rippon and G. M. Stallard, Iteration of a class of hyperbolic meromorphic functions,, Proc. Amer. Math. Soc., 127 (1999), 3251.
doi: 10.1090/S0002-9939-99-04942-4. |
[20] |
D. Ruelle, Repellers for real analytic maps,, Ergodic Th. Dyn. Sys., 2 (1982), 99.
doi: 10.1017/S0143385700009603. |
[21] |
G. M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions,, J. London Math. soc., 49 (1994), 281.
doi: 10.1112/jlms/49.2.281. |
[22] |
G. M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions II,, J. London Math. soc., 60 (1999), 847.
doi: 10.1112/S0024610799008029. |
[23] |
G. M. Stallard, Dimension of Julia sets of hyperbolic meromorphic functions,, Math. Proc. Camb. Phil. Soc., 127 (1999), 271.
doi: 10.1017/S0305004199003813. |
[24] |
G. M. Stallard, The Hausdorff dimension of Julia sets of hyperbolic meromorphic functions,, Ergodic Theory Dynam. Systems, 20 (2000), 895.
doi: 10.1017/S0143385700000481. |
[25] |
G. M. Stallard, Meromorphic functions whose Julia sets contain a free Jordan arc,, Ann. Acad. Sci. Fenn., 18 (1993), 273.
|
[26] |
N. Steinmetz, Rational Iterations,, Berlin: Walter de Gruyter, (1993).
doi: 10.1515/9783110889314. |
[27] |
D. Sullivan, Conformal dynamical systems: In Geometric dynamics,, Lecture Notes in Math., 1007 (1983), 725.
doi: 10.1007/BFb0061443. |
[28] |
O. Teichmüller, Eine Umkehrung des zweiten Hauptsatzes der Wertverteilungstheorie,, Deutsche Math., 2 (1937), 96. Google Scholar |
[29] |
L. A. Ter-Israelyan, Meromorphic functions of zero order with non-asymptotic deficient values,, Math. Zam., 13 (1973), 195.
|
[30] |
P. Walters, Invariant measures and equilibrium states for some mappings which expand distances,, Trans. Amer. Math. Soc., 236 (1978), 121.
doi: 10.1090/S0002-9947-1978-0466493-1. |
[31] |
M. Urbanski and A. Zdunik, The finer geometry and dynamics of exponential family,, Michingan Math. J., 51 (2003), 227.
doi: 10.1307/mmj/1060013195. |
[32] |
M. Urbanski and A. Zdunik, Real analyticity of Hausdorff dimension of finer Julia sets of exponential family,, Ergodic Th. and Dynam. Sys., 24 (2004), 279.
doi: 10.1017/S0143385703000208. |
[33] |
J. H. Zheng, Singularties and limit functions in iteration of meromorphic functions,, J. London Math. Soc., 67 (2003), 195.
doi: 10.1112/S0024610702003800. |
[34] |
J. H. Zheng, On transcendental meromorphic functions which are geometrically finite,, J. Austral. Math. Soc., 72 (2002), 93.
doi: 10.1017/S144678870000361X. |
[35] |
J. H. Zheng, Dynamics Of Meromorphic Functions, Monograph of Tsinghua University,, Tsinghua University Press, (2006). Google Scholar |
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