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Theory of $(a,b)$continued fraction transformations and applications
1.  Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 
2.  Department of Mathematical Sciences, DePaul University, 2320 N. Kenmore Ave., Chicago, IL 606143504 
[1] 
Marc Kessböhmer, Bernd O. Stratmann. On the asymptotic behaviour of the Lebesgue measure of sumlevel sets for continued fractions. Discrete & Continuous Dynamical Systems  A, 2012, 32 (7) : 24372451. doi: 10.3934/dcds.2012.32.2437 
[2] 
Laura Luzzi, Stefano Marmi. On the entropy of Japanese continued fractions. Discrete & Continuous Dynamical Systems  A, 2008, 20 (3) : 673711. doi: 10.3934/dcds.2008.20.673 
[3] 
Pierre Arnoux, Thomas A. Schmidt. Commensurable continued fractions. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 43894418. doi: 10.3934/dcds.2014.34.4389 
[4] 
Claudio Bonanno, Carlo Carminati, Stefano Isola, Giulio Tiozzo. Dynamics of continued fractions and kneading sequences of unimodal maps. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 13131332. doi: 10.3934/dcds.2013.33.1313 
[5] 
Élise Janvresse, Benoît Rittaud, Thierry de la Rue. Dynamics of $\lambda$continued fractions and $\beta$shifts. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 14771498. doi: 10.3934/dcds.2013.33.1477 
[6] 
Lulu Fang, Min Wu. Hausdorff dimension of certain sets arising in Engel continued fractions. Discrete & Continuous Dynamical Systems  A, 2018, 38 (5) : 23752393. doi: 10.3934/dcds.2018098 
[7] 
Doug Hensley. Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension. Discrete & Continuous Dynamical Systems  A, 2012, 32 (7) : 24172436. doi: 10.3934/dcds.2012.32.2417 
[8] 
Svetlana Katok, Ilie Ugarcovici. Structure of attractors for $(a,b)$continued fraction transformations. Journal of Modern Dynamics, 2010, 4 (4) : 637691. doi: 10.3934/jmd.2010.4.637 
[9] 
Wenzhi Luo, Zeév Rudnick, Peter Sarnak. The variance of arithmetic measures associated to closed geodesics on the modular surface. Journal of Modern Dynamics, 2009, 3 (2) : 271309. doi: 10.3934/jmd.2009.3.271 
[10] 
Jonathan C. Mattingly, Etienne Pardoux. Invariant measure selection by noise. An example. Discrete & Continuous Dynamical Systems  A, 2014, 34 (10) : 42234257. doi: 10.3934/dcds.2014.34.4223 
[11] 
Luis Barreira and Jorg Schmeling. Invariant sets with zero measure and full Hausdorff dimension. Electronic Research Announcements, 1997, 3: 114118. 
[12] 
Giuseppe Da Prato. An integral inequality for the invariant measure of some finite dimensional stochastic differential equation. Discrete & Continuous Dynamical Systems  B, 2016, 21 (9) : 30153027. doi: 10.3934/dcdsb.2016085 
[13] 
Paola Mannucci, Claudio Marchi, Nicoletta Tchou. Asymptotic behaviour for operators of Grushin type: Invariant measure and singular perturbations. Discrete & Continuous Dynamical Systems  S, 2019, 12 (1) : 119128. doi: 10.3934/dcdss.2019008 
[14] 
Boris Kalinin, Anatole Katok. Measure rigidity beyond uniform hyperbolicity: invariant measures for cartan actions on tori. Journal of Modern Dynamics, 2007, 1 (1) : 123146. doi: 10.3934/jmd.2007.1.123 
[15] 
Simon Lloyd, Edson Vargas. Critical covering maps without absolutely continuous invariant probability measure. Discrete & Continuous Dynamical Systems  A, 2019, 39 (5) : 23932412. doi: 10.3934/dcds.2019101 
[16] 
Yan Wang, Guanggan Chen. Invariant measure of stochastic fractional Burgers equation with degenerate noise on a bounded interval. Communications on Pure & Applied Analysis, 2019, 18 (6) : 31213135. doi: 10.3934/cpaa.2019140 
[17] 
Miguel Ângelo De Sousa Mendes. Quasiinvariant attractors of piecewise isometric systems. Discrete & Continuous Dynamical Systems  A, 2003, 9 (2) : 323338. doi: 10.3934/dcds.2003.9.323 
[18] 
Leonardo Mora. Homoclinic bifurcations, fat attractors and invariant curves. Discrete & Continuous Dynamical Systems  A, 2003, 9 (5) : 11331148. doi: 10.3934/dcds.2003.9.1133 
[19] 
Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Invariant manifolds as pullback attractors of nonautonomous differential equations. Discrete & Continuous Dynamical Systems  A, 2006, 15 (2) : 579596. doi: 10.3934/dcds.2006.15.579 
[20] 
Huyi Hu, Miaohua Jiang, Yunping Jiang. Infimum of the metric entropy of hyperbolic attractors with respect to the SRB measure. Discrete & Continuous Dynamical Systems  A, 2008, 22 (1&2) : 215234. doi: 10.3934/dcds.2008.22.215 
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