# American Institute of Mathematical Sciences

• Previous Article
Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field
• DCDS Home
• This Issue
• Next Article
Stability of the distribution function for piecewise monotonic maps on the interval
May  2018, 38(5): 2541-2554. doi: 10.3934/dcds.2018106

## Constant slope models for finitely generated maps

 Silesian University in Opava, Na Rybničku 626/1, 746 01 Opava, Czech Republic

Received  July 2017 Published  March 2018

We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying these conditions.

Citation: Samuel Roth. Constant slope models for finitely generated maps. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2541-2554. doi: 10.3934/dcds.2018106
##### References:

show all references

##### References:
The production of a finitely generated map
Some countably monotone maps from the literature -cf. Section 7.2
 Graph Source [3,§ 7.1] [4,§ 4] [9,§ 8] [3,§ 7.2.1] [3,§ 7.2.1] Vere-Jones classification Recurrent Transient Recurrent Recurrent Transient Finitely generated No No No Yes Yes Constant slope models None For all $\lambda\geq\exp h(f)$ For all $\lambda\geq\exp h(f)$ Unique, $\lambda=\exp h(f)$ None
 Graph Source [3,§ 7.1] [4,§ 4] [9,§ 8] [3,§ 7.2.1] [3,§ 7.2.1] Vere-Jones classification Recurrent Transient Recurrent Recurrent Transient Finitely generated No No No Yes Yes Constant slope models None For all $\lambda\geq\exp h(f)$ For all $\lambda\geq\exp h(f)$ Unique, $\lambda=\exp h(f)$ None
 [1] Lluís Alsedà, Michał Misiurewicz. Semiconjugacy to a map of a constant slope. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3403-3413. doi: 10.3934/dcdsb.2015.20.3403 [2] 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 [3] Christian Wolf. A shift map with a discontinuous entropy function. Discrete & Continuous Dynamical Systems, 2020, 40 (1) : 319-329. doi: 10.3934/dcds.2020012 [4] Mark F. Demers, Christopher J. Ianzano, Philip Mayer, Peter Morfe, Elizabeth C. Yoo. Limiting distributions for countable state topological Markov chains with holes. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 105-130. doi: 10.3934/dcds.2017005 [5] James P. Kelly, Kevin McGoff. Entropy conjugacy for Markov multi-maps of the interval. Discrete & Continuous Dynamical Systems, 2021, 41 (5) : 2071-2094. doi: 10.3934/dcds.2020353 [6] David Burguet. Examples of $\mathcal{C}^r$ interval map with large symbolic extension entropy. Discrete & Continuous Dynamical Systems, 2010, 26 (3) : 873-899. doi: 10.3934/dcds.2010.26.873 [7] José S. Cánovas. Topological sequence entropy of $\omega$–limit sets of interval maps. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 781-786. doi: 10.3934/dcds.2001.7.781 [8] Silvére Gangloff, Alonso Herrera, Cristobal Rojas, Mathieu Sablik. Computability of topological entropy: From general systems to transformations on Cantor sets and the interval. Discrete & Continuous Dynamical Systems, 2020, 40 (7) : 4259-4286. doi: 10.3934/dcds.2020180 [9] Prof. Dr.rer.nat Widodo. Topological entropy of shift function on the sequences space induced by expanding piecewise linear transformations. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 191-208. doi: 10.3934/dcds.2002.8.191 [10] Michael Jakobson, Lucia D. Simonelli. Countable Markov partitions suitable for thermodynamic formalism. Journal of Modern Dynamics, 2018, 13: 199-219. doi: 10.3934/jmd.2018018 [11] Yair Daon. Bernoullicity of equilibrium measures on countable Markov shifts. Discrete & Continuous Dynamical Systems, 2013, 33 (9) : 4003-4015. doi: 10.3934/dcds.2013.33.4003 [12] Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Thermodynamic formalism for random countable Markov shifts. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 131-164. doi: 10.3934/dcds.2008.22.131 [13] Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Corrigendum to: Thermodynamic formalism for random countable Markov shifts. Discrete & Continuous Dynamical Systems, 2015, 35 (1) : 593-594. doi: 10.3934/dcds.2015.35.593 [14] Yakov Pesin. On the work of Sarig on countable Markov chains and thermodynamic formalism. Journal of Modern Dynamics, 2014, 8 (1) : 1-14. doi: 10.3934/jmd.2014.8.1 [15] Michael Schraudner. Projectional entropy and the electrical wire shift. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 333-346. doi: 10.3934/dcds.2010.26.333 [16] Katrin Gelfert. Lower bounds for the topological entropy. Discrete & Continuous Dynamical Systems, 2005, 12 (3) : 555-565. doi: 10.3934/dcds.2005.12.555 [17] Jaume Llibre. Brief survey on the topological entropy. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3363-3374. doi: 10.3934/dcdsb.2015.20.3363 [18] Dongkui Ma, Min Wu. Topological pressure and topological entropy of a semigroup of maps. Discrete & Continuous Dynamical Systems, 2011, 31 (2) : 545-557 . doi: 10.3934/dcds.2011.31.545 [19] Piotr Oprocha, Paweł Potorski. Topological mixing, knot points and bounds of topological entropy. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3547-3564. doi: 10.3934/dcdsb.2015.20.3547 [20] Yuanhong Chen, Chao Ma, Jun Wu. Moving recurrent properties for the doubling map on the unit interval. Discrete & Continuous Dynamical Systems, 2016, 36 (6) : 2969-2979. doi: 10.3934/dcds.2016.36.2969

2020 Impact Factor: 1.392