International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 37-40, Pages 2019-2038
doi:10.1155/S016117120430428X
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
Abstract
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.