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,… (More)
We compute the K-groups for the Cuntz-Krieger algebras OA K(fµ) , where A K(fµ) is the Markov transition matrix arising from the kneading sequence K(fµ) of the one-parameter family of real quadratic maps fµ. Consider the one-parameter family of real quadratic maps f µ : [0, 1] → [0, 1] defined by f µ (x) = µx(1 − x), with µ ∈ [0, 4]. Using Milnor-Thurston's… (More)
We introduce the notion of conductance in discrete dynamical systems defined by iterated maps of the interval. Our starting point is the notion of conductance in the graph theory. We pretend to apply the known results in this new context.
Using the techniques developed in [ASR], we generalize to tree maps the Milnor and Thurston results about zeta function, semiconjugacy and topological entropy of interval maps. 1. Introduction Motivated by some applications concerning the study of two-dimensional real and one-dimensional complex dynamics, continuous maps from a tree into itself have been… (More)
Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and fast flow rate to avoid wall growth. However, these assumptions become unrealistic when the availability of a nutrient depends on the nutrient consumption rate and input nutrient concentration and when the flow rate is not fast enough.… (More)
The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence… (More)
Using the averaging theory of dynamical systems we describe in an analytical way the periodic structure and the stability of periodic orbits for the planar photogravitational hill problem. Moreover, we present a proof of the C 1 –non integrability for this problem.
We study a third-order partial differential equation in the form τu ttt + αu tt − c 2 u xx − bu xxt = 0, (1) that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures. In contrast with the current literature on the subject, we show that when the… (More)
The aim of this paper is to establish the existence of a "box-within-a-box" bifurcation structure for monotone families of Lorenz maps and to study its combi-natorics.