International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 38, Pages 2019-2038

Weighted kneading theory of one-dimensional maps with a hole

J. Leonel Rocha1 and J. Sousa Ramos2

1Secção de Matemática, Departamento de Engenharia Química, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, Lisboa 1949-014, Portugal
2Departamento de Matemática, Instituto Superior Técnico, avenida Rovisco Pais 1, Lisboa 1049-001, Portugal

Received 30 April 2003

Copyright © 2004 J. Leonel Rocha and J. Sousa Ramos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape rate.