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Almost periodic and almost automorphic solutions of linear differential equations
No invariant line fields on escaping sets of the family $\lambda e^{iz}+\gamma e^{-iz}$
1. | Department of Mathematics, Graduate Center, CUNY, 365 Fifth Avenue, New York, NY 10016, United States |
2. | Department of Mathematics, Queens College, Flushing, NY 11367, United States |
3. | Department of Mathematics, Nanjing University, Nanjing 210090, China |
References:
[1] |
M. Aspenberg and W. Bergweiler, Entire functions with Julia sets of positive measure, Math. Ann., 352 (2012), 27-54. |
[2] |
L. Carleson and T. Gamelin, "Complex Dynamics," Springer-Verlag, New York 1991. |
[3] |
B. Karpińska, Area and Hausdorff dimension of the set of accessible points of the Julia sets of $\lambda e^z$ and $\lambda\sin z$, Fund. Math., 159 (1999), 269-287. |
[4] |
A. E. Eremenko and M. Yu. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier (Grenoble), 42 (1992), 989-1020. |
[5] |
C. McMullen, Area and Hausdorff dimension of Julia sets of entire functions, Trans. Amer. Math. Soc., 300 (1987), 329-342. |
[6] |
C. McMullen, "Complex Dynamics and Renormalization," Ann. of Math. Studies, Vol. 135, 1994. |
[7] |
C. McMullen, Self-similarity of Siegel disk and Hausdorff dimension of Julia set, Acta Mathematica, 180 (1998), 247-292. |
[8] |
W. De Melo, P. Salomão, and E. Vargas, A full family of multimodel family of mappings on the circle, Ergodic Theory and Dynamical Systems, 31 (2011), 1325-1344.
doi: 10.1017/S0143385710000386. |
[9] |
L. Rempe, Rigidity of escaping dynamics for transdental entire functions, Acta Mathematica, 203 (2009), 235-267. |
[10] |
L. Rempe and S. van Strien, Absence of line fields and Mane's theorem for non-recurrent transcendental functions, Trans Amer. Math. Soc., 363 (2011), 203-228.
doi: 10.1090/S0002-9947-2010-05125-6. |
[11] |
D. Schleicher, The dynamical fine structure of iterated cosine maps and a dimension paradox, Duke Math. J., 136 (2007), 343-356.
doi: 10.1215/S0012-7094-07-13625-1. |
[12] |
H. Schubert, Area of Fatou sets of trigonometric functions, Proc. Amer. Math. Soc., 136 (2008), 1251-1259. |
[13] |
G. Zhang, On the non-escaping set of $e^{2\pi i\theta}sin(z)$, Israel J. Math., 165 (2008), 233-252. |
[14] |
G. Zhang, On the dynamics of $e^{2\pi i\theta}sin(z)$, Illinois J. Math., 49 (2005), 1171-1179. |
show all references
References:
[1] |
M. Aspenberg and W. Bergweiler, Entire functions with Julia sets of positive measure, Math. Ann., 352 (2012), 27-54. |
[2] |
L. Carleson and T. Gamelin, "Complex Dynamics," Springer-Verlag, New York 1991. |
[3] |
B. Karpińska, Area and Hausdorff dimension of the set of accessible points of the Julia sets of $\lambda e^z$ and $\lambda\sin z$, Fund. Math., 159 (1999), 269-287. |
[4] |
A. E. Eremenko and M. Yu. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier (Grenoble), 42 (1992), 989-1020. |
[5] |
C. McMullen, Area and Hausdorff dimension of Julia sets of entire functions, Trans. Amer. Math. Soc., 300 (1987), 329-342. |
[6] |
C. McMullen, "Complex Dynamics and Renormalization," Ann. of Math. Studies, Vol. 135, 1994. |
[7] |
C. McMullen, Self-similarity of Siegel disk and Hausdorff dimension of Julia set, Acta Mathematica, 180 (1998), 247-292. |
[8] |
W. De Melo, P. Salomão, and E. Vargas, A full family of multimodel family of mappings on the circle, Ergodic Theory and Dynamical Systems, 31 (2011), 1325-1344.
doi: 10.1017/S0143385710000386. |
[9] |
L. Rempe, Rigidity of escaping dynamics for transdental entire functions, Acta Mathematica, 203 (2009), 235-267. |
[10] |
L. Rempe and S. van Strien, Absence of line fields and Mane's theorem for non-recurrent transcendental functions, Trans Amer. Math. Soc., 363 (2011), 203-228.
doi: 10.1090/S0002-9947-2010-05125-6. |
[11] |
D. Schleicher, The dynamical fine structure of iterated cosine maps and a dimension paradox, Duke Math. J., 136 (2007), 343-356.
doi: 10.1215/S0012-7094-07-13625-1. |
[12] |
H. Schubert, Area of Fatou sets of trigonometric functions, Proc. Amer. Math. Soc., 136 (2008), 1251-1259. |
[13] |
G. Zhang, On the non-escaping set of $e^{2\pi i\theta}sin(z)$, Israel J. Math., 165 (2008), 233-252. |
[14] |
G. Zhang, On the dynamics of $e^{2\pi i\theta}sin(z)$, Illinois J. Math., 49 (2005), 1171-1179. |
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