We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an eigenvector of an operator acting on a space of measures. Then we give sufficient conditions under which this criterion is not satisfied. Finally, we give example...

BACKGROUND Oxytocin may cause adverse cardiovascular effects, including tachycardia and hypotension, whereas the optimal dose of oxytocin at elective cesarean section is unclear. To determine the lowest effective dose of oxytocin, we studied the hemodynamic effects of three doses during spinal anesthesia for elective single cesarean delivery. METHODS Sixty women received oxytocin by continuou...

Let Y be the space {z € C: z3 £ [0, 1]} with a metric defined by the arc length. Suppose that / is a continuous map from Y to itself and P is a finite /-invariant subset. In this paper we construct a continuous map C/> from Y to itself satisfying Cp\p = f\p which achieves the infimum topological entropies of continuous maps from Y to itself which agree with / on P .

Theorem A. Let g : [0, T ]× IR 7→ IR be a bounded function. (i) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is continuous for each t, then the Cauchy problem (1.1) has at least one solution. (ii) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is Lipschitz continuous for each t, with a uniform Lipschitz constant, then the Cauchy problem (1...

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...