# American Institute of Mathematical Sciences

November  2019, 39(11): 6241-6260. doi: 10.3934/dcds.2019272

## Escape dynamics for interval maps

 1 Centro de Investigação em Matemática e Aplicações, Dep. of Mathematics, Univ. de Évora, R. Romão Ramalho, 59, 7000-671 Évora, Portugal 2 Dep. of Mathematics, CAMGSD, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal

* Corresponding author

Received  October 2018 Revised  March 2019 Published  August 2019

Fund Project: Correia Ramos's work was partially supported by national funds through Fundação Nacional para a Ciência e a Tecnologia (FCT) of Portugal grant PEstOE/MAT/UI0117/2014 and the Centro de Investigação em Matemática e Aplicações of Univ. of Évora. The work of Martins and Pinto was partially supported by FCT/Portugal grant UID/MAT/04459/2013

We study the structure of the escape orbits for a certain class of interval maps. This structure is encoded in the escape transition matrix $\widehat{A}_f$ of an interval map $f$, extending the traditional matrix $A_f$ which considers the transition among the Markov subintervals. We show that the escape transition matrix is a topological conjugacy invariant. We then characterize the $0$–$1$ matrices that can be fabricated as escape transition matrices of Markov interval maps $f$ with escape sets. This shows the richness of this class of interval maps.

Citation: Carlos Correia Ramos, Nuno Martins, Paulo R. Pinto. Escape dynamics for interval maps. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6241-6260. doi: 10.3934/dcds.2019272
##### References:

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##### References:
Graph of the function in Example 2.4
Graph of the function $f$ in Example 2.9
Graph of the function $g_1$ in Example 2.9
Graph of the function $\phi_1$ in Example 2.9
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