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An introduction to piecewise smooth dynamics

By: Contributor(s): Material type: TextTextSeries: Advanced courses in mathematics: CRM BarcelonaPublication details: Birkhauser 2019 ChamDescription: vii, 129 p.: ill. Includes bibliographical referencesISBN:
  • 9783030236885
Subject(s): DDC classification:
  • 515.39 G5I6
Summary: This book is aimed at mathematicians, scientists, and engineers, studying models that involve a discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided into two complementary courses: piecewise smooth flows and maps, respectively. Starting from well known theoretical results, the authors bring the reader into the latest challenges in the field, going through stability analysis, bifurcation, singularities, decomposition theorems and an introduction to kneading theory. Both courses contain many examples which illustrate the theoretical concepts that are introduced. https://www.springer.com/gp/book/9783030236885
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Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-A / Slot 1377 (0 Floor, East Wing) Non-fiction General Stacks 515.39 G5I6 (Browse shelf(Opens below)) Available 201689

Table of Contents

1.Piecewise-smooth Flows /​ Mike R. Jeffrey
1.1.Introduction
1.2.History and applications
1.3.Inclusions and combinations
1.4.Types of dynamics
1.5.Switching layers
1.6.Multiple switches
1.7.Codimension r switching layers
1.8.Codimension r sliding
1.9.Boundary equilibrium bifurcations
1.10.Stability, equivalence, and bifurcation
1.11.Discontinuity-induced phenomena
1.12.Determinacy-breaking
1.13.Hidden attractors
1.14.Hidden bifurcations
1.15.Moving forward
2.Piecewise-smooth Maps /​ Paul Glendinning
2.1.Introduction to maps
2.2.Smooth theory
2.3.Piecewise-smooth maps of the interval
2.4.Lorenz maps and rotations
2.5.Gluing bifurcations
2.6.Piecewise-smooth maps of the plane
2.7.Periodic orbits and resonance
2.8.Robust chaos
2.9.Two-dimensional attractors
2.10.Challenges.

This book is aimed at mathematicians, scientists, and engineers, studying models that involve a discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided into two complementary courses: piecewise smooth flows and maps, respectively. Starting from well known theoretical results, the authors bring the reader into the latest challenges in the field, going through stability analysis, bifurcation, singularities, decomposition theorems and an introduction to kneading theory. Both courses contain many examples which illustrate the theoretical concepts that are introduced.

https://www.springer.com/gp/book/9783030236885

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