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Expanding interval maps with intermittent behaviour, physical measures and time scales
The construction of chaotic maps in the sense of Devaney on dendrites which commute to continuous maps on the unit interval
1. | Department of General Education for the Hearing Impaired, Tsukuba College of Technology, Ibaraki 305-0005, Japan |
2. | Institute of Mathematics, University of Tsukuba, Ibraki 305-8571, Japan |
[1] |
Tatsuya Arai. The structure of dendrites constructed by pointwise P-expansive maps on the unit interval. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 43-61. doi: 10.3934/dcds.2016.36.43 |
[2] |
Fernando Lenarduzzi. Recoding the classical Hénon-Devaney map. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4073-4092. doi: 10.3934/dcds.2020172 |
[3] |
Vladimír Špitalský. Entropy and exact Devaney chaos on totally regular continua. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3135-3152. doi: 10.3934/dcds.2013.33.3135 |
[4] |
Steven M. Pederson. Non-turning Poincaré map and homoclinic tangencies in interval maps with non-constant topological entropy. Conference Publications, 2001, 2001 (Special) : 295-302. doi: 10.3934/proc.2001.2001.295 |
[5] |
Katrin Gelfert. Lower bounds for the topological entropy. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 555-565. doi: 10.3934/dcds.2005.12.555 |
[6] |
Jaume Llibre. Brief survey on the topological entropy. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3363-3374. doi: 10.3934/dcdsb.2015.20.3363 |
[7] |
Christian Wolf. A shift map with a discontinuous entropy function. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 319-329. doi: 10.3934/dcds.2020012 |
[8] |
Alfonso Artigue. Discrete and continuous topological dynamics: Fields of cross sections and expansive flows. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 5911-5927. doi: 10.3934/dcds.2016059 |
[9] |
Dongkui Ma, Min Wu. Topological pressure and topological entropy of a semigroup of maps. Discrete and Continuous Dynamical Systems, 2011, 31 (2) : 545-557 . doi: 10.3934/dcds.2011.31.545 |
[10] |
Piotr Oprocha, Paweł Potorski. Topological mixing, knot points and bounds of topological entropy. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3547-3564. doi: 10.3934/dcdsb.2015.20.3547 |
[11] |
Boris Hasselblatt, Zbigniew Nitecki, James Propp. Topological entropy for nonuniformly continuous maps. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 201-213. doi: 10.3934/dcds.2008.22.201 |
[12] |
Michał Misiurewicz. On Bowen's definition of topological entropy. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 827-833. doi: 10.3934/dcds.2004.10.827 |
[13] |
Lluís Alsedà, David Juher, Francesc Mañosas. Forward triplets and topological entropy on trees. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 623-641. doi: 10.3934/dcds.2021131 |
[14] |
B. Fernandez, P. Guiraud. Route to chaotic synchronisation in coupled map lattices: Rigorous results. Discrete and Continuous Dynamical Systems - B, 2004, 4 (2) : 435-456. doi: 10.3934/dcdsb.2004.4.435 |
[15] |
Jan Philipp Schröder. Ergodicity and topological entropy of geodesic flows on surfaces. Journal of Modern Dynamics, 2015, 9: 147-167. doi: 10.3934/jmd.2015.9.147 |
[16] |
Xiaomin Zhou. Relative entropy dimension of topological dynamical systems. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6631-6642. doi: 10.3934/dcds.2019288 |
[17] |
Yun Zhao, Wen-Chiao Cheng, Chih-Chang Ho. Q-entropy for general topological dynamical systems. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2059-2075. doi: 10.3934/dcds.2019086 |
[18] |
Eva Glasmachers, Gerhard Knieper, Carlos Ogouyandjou, Jan Philipp Schröder. Topological entropy of minimal geodesics and volume growth on surfaces. Journal of Modern Dynamics, 2014, 8 (1) : 75-91. doi: 10.3934/jmd.2014.8.75 |
[19] |
Dante Carrasco-Olivera, Roger Metzger Alvan, Carlos Arnoldo Morales Rojas. Topological entropy for set-valued maps. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3461-3474. doi: 10.3934/dcdsb.2015.20.3461 |
[20] |
Yujun Ju, Dongkui Ma, Yupan Wang. Topological entropy of free semigroup actions for noncompact sets. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 995-1017. doi: 10.3934/dcds.2019041 |
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