American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 903-912. doi: 10.3934/proc.2011.2011.903

Minimality in iterative systems of Möbius transformations

Petr Kůrka 1,

1. 

Center for Theoretical Study, Academy of Sciences and Charles University in Prague, Jilská 1, CZ-11000 Praha 1

Received  July 2010 Revised  March 2011 Published  October 2011

We study the parameter space of an iterative system consisting of two hyperbolic disc Möbius transformations. We identify several classes of parameters which yield discrete groups whose fundamental polygons have sides at the Euclidean boundary. It follows that these system are not minimal.
Keywords: iterative Möbius systems, topological dynamics, minimal systems.
Mathematics Subject Classification: Primary: 54H20; Secondary: 37F30.
Citation: Petr Kůrka. Minimality in iterative systems of Möbius transformations. Conference Publications, 2011, 2011 (Special) : 903-912. doi: 10.3934/proc.2011.2011.903
[1]

Petr Kůrka. Iterative systems of real Möbius transformations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 567-574. doi: 10.3934/dcds.2009.25.567
[2]

Wen Huang, Zhiren Wang, Guohua Zhang. Möbius disjointness for topological models of ergodic systems with discrete spectrum. Journal of Modern Dynamics, 2019, 14: 277-290. doi: 10.3934/jmd.2019010
[3]

Fangzhou Cai, Song Shao. Topological characteristic factors along cubes of minimal systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 5301-5317. doi: 10.3934/dcds.2019216
[4]

Philipp Reiter. Regularity theory for the Möbius energy. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1463-1471. doi: 10.3934/cpaa.2010.9.1463
[5]

Konovenko Nadiia, Lychagin Valentin. Möbius invariants in image recognition. Journal of Geometric Mechanics, 2017, 9 (2) : 191-206. doi: 10.3934/jgm.2017008
[6]

Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1
[7]

Morten Brøns. An iterative method for the canard explosion in general planar systems. Conference Publications, 2013, 2013 (special) : 77-83. doi: 10.3934/proc.2013.2013.77
[8]

Alfredo Marzocchi, Sara Zandonella Necca. Attractors for dynamical systems in topological spaces. Discrete & Continuous Dynamical Systems - A, 2002, 8 (3) : 585-597. doi: 10.3934/dcds.2002.8.585
[9]

Patrick Bonckaert, Timoteo Carletti, Ernest Fontich. On dynamical systems close to a product of $m$ rotations. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 349-366. doi: 10.3934/dcds.2009.24.349
[10]

K. Tintarev. Critical values and minimal periods for autonomous Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 1995, 1 (3) : 389-400. doi: 10.3934/dcds.1995.1.389
[11]

Frank Blume. Minimal rates of entropy convergence for rank one systems. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 773-796. doi: 10.3934/dcds.2000.6.773
[12]

Jean-Luc Chabert, Ai-Hua Fan, Youssef Fares. Minimal dynamical systems on a discrete valuation domain. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 777-795. doi: 10.3934/dcds.2009.25.777
[13]

Piotr Oprocha. Double minimality, entropy and disjointness with all minimal systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 263-275. doi: 10.3934/dcds.2019011
[14]

Rich Stankewitz, Hiroki Sumi. Backward iteration algorithms for Julia sets of Möbius semigroups. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6475-6485. doi: 10.3934/dcds.2016079
[15]

Jon Chaika, Alex Eskin. Möbius disjointness for interval exchange transformations on three intervals. Journal of Modern Dynamics, 2019, 14: 55-86. doi: 10.3934/jmd.2019003
[16]

Livio Flaminio, Giovanni Forni. Orthogonal powers and Möbius conjecture for smooth time changes of horocycle flows. Electronic Research Announcements, 2019, 26: 16-23. doi: 10.3934/era.2019.26.002
[17]

Marian Gidea, Rafael De La Llave. Topological methods in the instability problem of Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2006, 14 (2) : 295-328. doi: 10.3934/dcds.2006.14.295
[18]

Adriano Da Silva, Alexandre J. Santana, Simão N. Stelmastchuk. Topological conjugacy of linear systems on Lie groups. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3411-3421. doi: 10.3934/dcds.2017144
[19]

Yun Zhao, Wen-Chiao Cheng, Chih-Chang Ho. Q-entropy for general topological dynamical systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 2059-2075. doi: 10.3934/dcds.2019086
[20]

Chao Ma, Baowei Wang, Jun Wu. Diophantine approximation of the orbits in topological dynamical systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2455-2471. doi: 10.3934/dcds.2019104

 Impact Factor: 

Tools

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences