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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 and Continuous Dynamical Systems, 2012, 32 (7) : 24372451. doi: 10.3934/dcds.2012.32.2437 
[2] 
Laura Luzzi, Stefano Marmi. On the entropy of Japanese continued fractions. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 673711. doi: 10.3934/dcds.2008.20.673 
[3] 
Pierre Arnoux, Thomas A. Schmidt. Commensurable continued fractions. Discrete and Continuous Dynamical Systems, 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 and Continuous Dynamical Systems, 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 and Continuous Dynamical Systems, 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 and Continuous Dynamical Systems, 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 and Continuous Dynamical Systems, 2012, 32 (7) : 24172436. doi: 10.3934/dcds.2012.32.2417 
[8] 
Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 63096330. doi: 10.3934/dcds.2020281 
[9] 
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 
[10] 
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 
[11] 
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 
[12] 
Jonathan C. Mattingly, Etienne Pardoux. Invariant measure selection by noise. An example. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 42234257. doi: 10.3934/dcds.2014.34.4223 
[13] 
Luis Barreira and Jorg Schmeling. Invariant sets with zero measure and full Hausdorff dimension. Electronic Research Announcements, 1997, 3: 114118. 
[14] 
Miguel Ângelo De Sousa Mendes. Quasiinvariant attractors of piecewise isometric systems. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 323338. doi: 10.3934/dcds.2003.9.323 
[15] 
Leonardo Mora. Homoclinic bifurcations, fat attractors and invariant curves. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 11331148. doi: 10.3934/dcds.2003.9.1133 
[16] 
Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Invariant manifolds as pullback attractors of nonautonomous differential equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 579596. doi: 10.3934/dcds.2006.15.579 
[17] 
Simon Lloyd, Edson Vargas. Critical covering maps without absolutely continuous invariant probability measure. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 23932412. doi: 10.3934/dcds.2019101 
[18] 
Giuseppe Da Prato. An integral inequality for the invariant measure of some finite dimensional stochastic differential equation. Discrete and Continuous Dynamical Systems  B, 2016, 21 (9) : 30153027. doi: 10.3934/dcdsb.2016085 
[19] 
Paola Mannucci, Claudio Marchi, Nicoletta Tchou. Asymptotic behaviour for operators of Grushin type: Invariant measure and singular perturbations. Discrete and Continuous Dynamical Systems  S, 2019, 12 (1) : 119128. doi: 10.3934/dcdss.2019008 
[20] 
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 
2020 Impact Factor: 0.929
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