Eur. Phys. J. Special Topics 222, 285-301 (2013)
https://doi.org/10.1140/epjst/e2013-01842-y

Regular Article

Invariants for the topological characterization of the iteration of differentiable functions – the bimodal case

CIMA-UE, Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal

^a e-mail: mfac@uevora.pt
^b e-mail: ccr@uevora.pt
^c e-mail: smv@uevora.pt

Received: 27 March 2013
Revised: 25 April 2013
Published online: 25 June 2013

Abstract

We consider dynamical systems defined by a particular class of differentiable functions, as fixed state space. The dynamics is given by the iteration of an operator induced by a polynomial map which belongs to an appropriate family of isentropic bimodal interval maps. We characterize topologically these dynamical systems, in particular using the invariants defined for the iteration of the bimodal interval maps.