Descriptive Topology in Selected Topics of Functional Analysis

Descriptive Topology in Selected Topics of Functional Analysis


by Jerzy Kakol; Wieslaw Kubis; Manuel López-Pellicer

Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. Neimark-Sacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

Springer US; August 2011 493 pages; ISBN 9781461405290 Read online , or download in secure PDF format Title: Descriptive Topology in Selected Topics of Functional Analysis Author: Jerzy Kakol; Wieslaw Kubis; Manuel López-Pellicer   Buy, download and read Descriptive Topology in Selected Topics of Functional Analysis (eBook) by Jerzy Kakol; Wieslaw Kubis; Manuel López-Pellicer today!
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