abstract
- In this article we introduce a one-parameter family of skew product (Gt)t ∈ [−ε, ε] maps exhibiting a heterodimensional cycle such that the number of isolated periodic orbits inside it has not super-exponential growth. The dynamics in the central direction of the maps Gt is described by a one-parameter family of system of iterated functions.
- This work is part of the PhD thesis of the author, under the supervision of Lorenzo Diaz and Jorge Rocha. The author thanks Professors Lorenzo Diaz and Jorge Rocha, for having proposed this topic, by the stimulating conversations, the guidance and useful suggestions. This research was funded by by the Portuguese government through the FCT (Fundação para a Ciência e a Tecnologia) under the project PTDC/MAT/099493/2008. The author was supported by the grants SFRH/BD/27674/2006 and SFRH/BD/49735/2009 of FCT.