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Variational proof for hard Discrete breathers in some classes of Hamiltonian dynamical systems
Accessible points in the Julia sets of stable exponentials
1.  Department of Mathematics and Statistics, Boston University, 111 Cumminton St., Boston, MA 02215, United States, United States, United States, United States 
2.  Department of Mathematics and Statistics, Boston University, 111 Cummington St., Boston, MA 02215, United States 
[1] 
Weiyuan Qiu, Fei Yang, Yongcheng Yin. Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps. Discrete & Continuous Dynamical Systems, 2016, 36 (6) : 33753416. doi: 10.3934/dcds.2016.36.3375 
[2] 
Leticia PardoSimón. Criniferous entire maps with absorbing Cantor bouquets. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021144 
[3] 
S. Astels. Thickness measures for Cantor sets. Electronic Research Announcements, 1999, 5: 108111. 
[4] 
Mehdi Pourbarat. On the arithmetic difference of middle Cantor sets. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 42594278. doi: 10.3934/dcds.2018186 
[5] 
Koh Katagata. Quartic Julia sets including any two copies of quadratic Julia sets. Discrete & Continuous Dynamical Systems, 2016, 36 (4) : 21032112. doi: 10.3934/dcds.2016.36.2103 
[6] 
Luiz Henrique de Figueiredo, Diego Nehab, Jorge Stolfi, João Batista S. de Oliveira. Rigorous bounds for polynomial Julia sets. Journal of Computational Dynamics, 2016, 3 (2) : 113137. doi: 10.3934/jcd.2016006 
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Robert L. Devaney, Daniel M. Look. Buried Sierpinski curve Julia sets. Discrete & Continuous Dynamical Systems, 2005, 13 (4) : 10351046. doi: 10.3934/dcds.2005.13.1035 
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Danilo Antonio Caprio. A class of adding machines and Julia sets. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 59515970. doi: 10.3934/dcds.2016061 
[9] 
Nathaniel D. Emerson. Dynamics of polynomials with disconnected Julia sets. Discrete & Continuous Dynamical Systems, 2003, 9 (4) : 801834. doi: 10.3934/dcds.2003.9.801 
[10] 
TienCuong Dinh, Nessim Sibony. Rigidity of Julia sets for Hénon type maps. Journal of Modern Dynamics, 2014, 8 (3&4) : 499548. doi: 10.3934/jmd.2014.8.499 
[11] 
Tarik Aougab, Stella Chuyue Dong, Robert S. Strichartz. Laplacians on a family of quadratic Julia sets II. Communications on Pure & Applied Analysis, 2013, 12 (1) : 158. doi: 10.3934/cpaa.2013.12.1 
[12] 
Krzysztof Barański, Michał Wardal. On the Hausdorff dimension of the Sierpiński Julia sets. Discrete & Continuous Dynamical Systems, 2015, 35 (8) : 32933313. doi: 10.3934/dcds.2015.35.3293 
[13] 
Ali Messaoudi, Rafael Asmat Uceda. Stochastic adding machine and $2$dimensional Julia sets. Discrete & Continuous Dynamical Systems, 2014, 34 (12) : 52475269. doi: 10.3934/dcds.2014.34.5247 
[14] 
Doug Hensley. Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension. Discrete & Continuous Dynamical Systems, 2012, 32 (7) : 24172436. doi: 10.3934/dcds.2012.32.2417 
[15] 
Silvére Gangloff, Alonso Herrera, Cristobal Rojas, Mathieu Sablik. Computability of topological entropy: From general systems to transformations on Cantor sets and the interval. Discrete & Continuous Dynamical Systems, 2020, 40 (7) : 42594286. doi: 10.3934/dcds.2020180 
[16] 
Koh Katagata. Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of quadratic Julia sets. Discrete & Continuous Dynamical Systems, 2019, 39 (9) : 53195337. doi: 10.3934/dcds.2019217 
[17] 
Rich Stankewitz, Hiroki Sumi. Random backward iteration algorithm for Julia sets of rational semigroups. Discrete & Continuous Dynamical Systems, 2015, 35 (5) : 21652175. doi: 10.3934/dcds.2015.35.2165 
[18] 
Rich Stankewitz, Hiroki Sumi. Backward iteration algorithms for Julia sets of Möbius semigroups. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 64756485. doi: 10.3934/dcds.2016079 
[19] 
Alexander Blokh, Lex Oversteegen, Vladlen Timorin. Nondegenerate locally connected models for plane continua and Julia sets. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 57815795. doi: 10.3934/dcds.2017251 
[20] 
Youming Wang, Fei Yang, Song Zhang, Liangwen Liao. Escape quartered theorem and the connectivity of the Julia sets of a family of rational maps. Discrete & Continuous Dynamical Systems, 2019, 39 (9) : 51855206. doi: 10.3934/dcds.2019211 
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