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One dimensional Dirac equation with quadratic nonlinearities
The dynamics and geometry of the Fatou functions
1.  Faculty of Mathematics & Information Sciences, Warsaw University of Technology, Plac Politechnki 1, Warsaw 00661, Poland 
2.  Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 762031430 
[1] 
Jon Chaika. Hausdorff dimension for ergodic measures of interval exchange transformations. Journal of Modern Dynamics, 2008, 2 (3) : 457464. doi: 10.3934/jmd.2008.2.457 
[2] 
Thomas Jordan, Mark Pollicott. The Hausdorff dimension of measures for iterated function systems which contract on average. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 235246. doi: 10.3934/dcds.2008.22.235 
[3] 
Krzysztof Barański, Michał Wardal. On the Hausdorff dimension of the Sierpiński Julia sets. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 32933313. doi: 10.3934/dcds.2015.35.3293 
[4] 
Sabyasachi Mukherjee. Parabolic arcs of the multicorns: Realanalyticity of Hausdorff dimension, and singularities of $\mathrm{Per}_n(1)$ curves. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 25652588. doi: 10.3934/dcds.2017110 
[5] 
Paul Wright. Differentiability of Hausdorff dimension of the nonwandering set in a planar open billiard. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 39934014. doi: 10.3934/dcds.2016.36.3993 
[6] 
Hiroki Sumi, Mariusz Urbański. Bowen parameter and Hausdorff dimension for expanding rational semigroups. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 25912606. doi: 10.3934/dcds.2012.32.2591 
[7] 
Sara Munday. On Hausdorff dimension and cusp excursions for Fuchsian groups. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 25032520. doi: 10.3934/dcds.2012.32.2503 
[8] 
Shmuel Friedland, Gunter Ochs. Hausdorff dimension, strong hyperbolicity and complex dynamics. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 405430. doi: 10.3934/dcds.1998.4.405 
[9] 
Luis Barreira and Jorg Schmeling. Invariant sets with zero measure and full Hausdorff dimension. Electronic Research Announcements, 1997, 3: 114118. 
[10] 
Kanji Inui, Hikaru Okada, Hiroki Sumi. The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 753766. doi: 10.3934/dcds.2020060 
[11] 
Manuel FernándezMartínez, Miguel Ángel López Guerrero. Generating prefractals to approach real IFSattractors with a fixed Hausdorff dimension. Discrete and Continuous Dynamical Systems  S, 2015, 8 (6) : 11291137. doi: 10.3934/dcdss.2015.8.1129 
[12] 
Stefan Klus, Péter Koltai, Christof Schütte. On the numerical approximation of the PerronFrobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (1) : 5179. doi: 10.3934/jcd.2016003 
[13] 
Yan Huang. On Hausdorff dimension of the set of nonergodic directions of twogenus double cover of tori. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 23952409. doi: 10.3934/dcds.2018099 
[14] 
Lulu Fang, Min Wu. Hausdorff dimension of certain sets arising in Engel continued fractions. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 23752393. doi: 10.3934/dcds.2018098 
[15] 
Vanderlei Horita, Marcelo Viana. Hausdorff dimension for nonhyperbolic repellers II: DA diffeomorphisms. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 11251152. doi: 10.3934/dcds.2005.13.1125 
[16] 
Krzysztof Barański. Hausdorff dimension of selfaffine limit sets with an invariant direction. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 10151023. doi: 10.3934/dcds.2008.21.1015 
[17] 
Doug Hensley. Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 24172436. doi: 10.3934/dcds.2012.32.2417 
[18] 
Carlos Matheus, Jacob Palis. An estimate on the Hausdorff dimension of stable sets of nonuniformly hyperbolic horseshoes. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 431448. doi: 10.3934/dcds.2018020 
[19] 
Aline Cerqueira, Carlos Matheus, Carlos Gustavo Moreira. Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra. Journal of Modern Dynamics, 2018, 12: 151174. doi: 10.3934/jmd.2018006 
[20] 
Cristina Lizana, Leonardo Mora. Lower bounds for the Hausdorff dimension of the geometric Lorenz attractor: The homoclinic case. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 699709. doi: 10.3934/dcds.2008.22.699 
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