The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Um estudo sobre a resolução de problemas e suas relações com a afetividade

This research aims at examining the relationship between the performance of elementary school students Cycle I in problem solving and attitudes toward mathematics. For this, a research was conducted at a state school in the city of Bauru which was selected for convenience. Participants were randomly selected consisting of 75 students, of whom 21 were third years and 57 were of three classes of fifth year. The instruments used for data collection were: a informative questionnaire to characterize the students in age, grade, favorite subjects and the least liked, among others, an attitude scale, Likert type, to examine the attitudes toward mathematics; a interviews with 11 selected students according to scores on the attitudes and mathematical problems to be solved through the method of thinking aloud. The results showed that the major difficulties encountered by students in solving problems were: to understand the problems, formalizing the reasoning, recognize in the problem the algorithms needed for its resolution, make calculations with decimal numbers, do combinatorics, using the sum of equal portions instead of multiplying, self-confidence and autonomy in what he was doing, and others; participants with positive attitudes towards mathematics showed greater confidence to solve problems as well as a greater understanding on what was required by them, but were not detected significant relation between the attitudes and performance, since it was unfavorable