-
Previous Article
The Cauchy problem for a nonhomogeneous heat equation with reaction
- DCDS Home
- This Issue
-
Next Article
Propagation of long-crested water waves
Non-autonomous Julia sets with measurable invariant sequences of line fields
1. | Department of Mathematics,University of Rhode Island, 5 Lippitt Road, Room 102F, Kingston, RI 02881, United States |
References:
[1] |
L. Carleson and T. W. Gamelin, "Complex Dynamics,'', Springer Verlag, (1993).
|
[2] |
M. Comerford, "Properties of Julia Sets for The Arbitrary Composition of Monic Polynomials with Uniformly Bounded Coefficients,'', Ph. D. Thesis, (2001). Google Scholar |
[3] |
M. Comerford, A survey of results in random iteration,, Proceedings Symposia in Pure Mathematics, (2004).
|
[4] |
M. Comerford, Conjugacy and counterexample in random iteration,, Pac. J. of Math., 211 (2003), 69.
doi: 10.2140/pjm.2003.211.69. |
[5] |
A. È. Erëmenko and M. J. Lyubich, Examples of entire functions with pathological dynamics,, J. London Math. Soc. (2), 36 (1987), 458.
|
[6] |
J. E. Fornaess and N. Sibony, Random iterations of rational functions,, Ergodic Theory Dynamical Systems, 11 (1991), 687.
doi: 10.1017/S0143385700006428. |
[7] |
Curtis T. McMullen, "Complex Dynamics and Renormalization,", Annals of Mathematics Study 135, (1994).
|
[8] |
Curtis T. McMullen, Frontiers in complex dynamics,, Bull. Amer. Math. Soc., 31 (1994), 155.
|
[9] |
R. Ma né, P. Sad and D. Sullivan, On the dynamics of rational maps,, Ann. Sc. de l'Ecole Normale Supérieure, 16 (1983), 193.
|
[10] |
L. Rempe and S. Van Strien, Absence of line fields and Ma né's theorem for nonrecurrent transcendental functions,, Transactions of the American Mathematical Society, 363 (2011), 203.
doi: 10.1090/S0002-9947-2010-05125-6. |
[11] |
Xiaoguang Wang, Rational maps admitting meromorphic invariant line fields,, Bull. Aust. Math. Soc., 80 (2009), 454.
doi: 10.1017/S0004972709000495. |
show all references
References:
[1] |
L. Carleson and T. W. Gamelin, "Complex Dynamics,'', Springer Verlag, (1993).
|
[2] |
M. Comerford, "Properties of Julia Sets for The Arbitrary Composition of Monic Polynomials with Uniformly Bounded Coefficients,'', Ph. D. Thesis, (2001). Google Scholar |
[3] |
M. Comerford, A survey of results in random iteration,, Proceedings Symposia in Pure Mathematics, (2004).
|
[4] |
M. Comerford, Conjugacy and counterexample in random iteration,, Pac. J. of Math., 211 (2003), 69.
doi: 10.2140/pjm.2003.211.69. |
[5] |
A. È. Erëmenko and M. J. Lyubich, Examples of entire functions with pathological dynamics,, J. London Math. Soc. (2), 36 (1987), 458.
|
[6] |
J. E. Fornaess and N. Sibony, Random iterations of rational functions,, Ergodic Theory Dynamical Systems, 11 (1991), 687.
doi: 10.1017/S0143385700006428. |
[7] |
Curtis T. McMullen, "Complex Dynamics and Renormalization,", Annals of Mathematics Study 135, (1994).
|
[8] |
Curtis T. McMullen, Frontiers in complex dynamics,, Bull. Amer. Math. Soc., 31 (1994), 155.
|
[9] |
R. Ma né, P. Sad and D. Sullivan, On the dynamics of rational maps,, Ann. Sc. de l'Ecole Normale Supérieure, 16 (1983), 193.
|
[10] |
L. Rempe and S. Van Strien, Absence of line fields and Ma né's theorem for nonrecurrent transcendental functions,, Transactions of the American Mathematical Society, 363 (2011), 203.
doi: 10.1090/S0002-9947-2010-05125-6. |
[11] |
Xiaoguang Wang, Rational maps admitting meromorphic invariant line fields,, Bull. Aust. Math. Soc., 80 (2009), 454.
doi: 10.1017/S0004972709000495. |
[1] |
Kaixuan Zhu, Ji Li, Yongqin Xie, Mingji Zhang. Dynamics of non-autonomous fractional reaction-diffusion equations on $ \mathbb{R}^{N} $ driven by multiplicative noise. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020376 |
[2] |
Yanan Li, Zhijian Yang, Na Feng. Uniform attractors and their continuity for the non-autonomous Kirchhoff wave models. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021018 |
[3] |
Yangrong Li, Shuang Yang, Qiangheng Zhang. Odd random attractors for stochastic non-autonomous Kuramoto-Sivashinsky equations without dissipation. Electronic Research Archive, 2020, 28 (4) : 1529-1544. doi: 10.3934/era.2020080 |
[4] |
Pengyu Chen. Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020383 |
[5] |
Lin Shi, Xuemin Wang, Dingshi Li. Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5367-5386. doi: 10.3934/cpaa.2020242 |
[6] |
Pengyu Chen, Yongxiang Li, Xuping Zhang. Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1531-1547. doi: 10.3934/dcdsb.2020171 |
[7] |
Wenqiang Zhao, Yijin Zhang. High-order Wong-Zakai approximations for non-autonomous stochastic $ p $-Laplacian equations on $ \mathbb{R}^N $. Communications on Pure & Applied Analysis, 2021, 20 (1) : 243-280. doi: 10.3934/cpaa.2020265 |
[8] |
Parikshit Upadhyaya, Elias Jarlebring, Emanuel H. Rubensson. A density matrix approach to the convergence of the self-consistent field iteration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 99-115. doi: 10.3934/naco.2020018 |
[9] |
Hua Shi, Xiang Zhang, Yuyan Zhang. Complex planar Hamiltonian systems: Linearization and dynamics. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020406 |
[10] |
Yancong Xu, Lijun Wei, Xiaoyu Jiang, Zirui Zhu. Complex dynamics of a SIRS epidemic model with the influence of hospital bed number. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021016 |
[11] |
Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen, Chih-Her Chen. On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3291-3304. doi: 10.3934/dcds.2020127 |
[12] |
Dan Zhu, Rosemary A. Renaut, Hongwei Li, Tianyou Liu. Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory. Inverse Problems & Imaging, 2021, 15 (1) : 159-183. doi: 10.3934/ipi.2020076 |
[13] |
Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 27-43. doi: 10.3934/naco.2020013 |
[14] |
José Madrid, João P. G. Ramos. On optimal autocorrelation inequalities on the real line. Communications on Pure & Applied Analysis, 2021, 20 (1) : 369-388. doi: 10.3934/cpaa.2020271 |
[15] |
Tommi Brander, Joonas Ilmavirta, Petteri Piiroinen, Teemu Tyni. Optimal recovery of a radiating source with multiple frequencies along one line. Inverse Problems & Imaging, 2020, 14 (6) : 967-983. doi: 10.3934/ipi.2020044 |
[16] |
Álvaro Castañeda, Pablo González, Gonzalo Robledo. Topological Equivalence of nonautonomous difference equations with a family of dichotomies on the half line. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020278 |
[17] |
Weisong Dong, Chang Li. Second order estimates for complex Hessian equations on Hermitian manifolds. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020377 |
[18] |
Tuoc Phan, Grozdena Todorova, Borislav Yordanov. Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1071-1099. doi: 10.3934/dcds.2020310 |
[19] |
M. S. Lee, H. G. Harno, B. S. Goh, K. H. Lim. On the bang-bang control approach via a component-wise line search strategy for unconstrained optimization. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 45-61. doi: 10.3934/naco.2020014 |
[20] |
Yohei Yamazaki. Center stable manifolds around line solitary waves of the Zakharov–Kuznetsov equation with critical speed. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021008 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]