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 in 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.
| Introduction |
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1 | (2) |
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3 | (52) |
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3 | (4) |
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1.2 History and applications |
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7 | (3) |
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1.3 Inclusions and combinations |
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10 | (5) |
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15 | (8) |
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23 | (7) |
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30 | (2) |
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1.7 Codimension r switching layers |
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32 | (1) |
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1.8 Codimension r sliding |
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33 | (3) |
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1.9 Boundary equilibrium bifurcations |
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36 | (2) |
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1.10 Stability, equivalence, and bifurcation |
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38 | (4) |
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1.11 Discontinuity-induced phenomena |
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42 | (7) |
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1.12 Determinacy-breaking |
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49 | (1) |
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50 | (1) |
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51 | (1) |
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52 | (3) |
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55 | (68) |
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55 | (5) |
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60 | (9) |
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2.3 Piecewise-smooth maps of the interval |
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69 | (14) |
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2.4 Lorenz maps and rotations |
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83 | (8) |
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91 | (6) |
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2.6 Piecewise-smooth maps of the plane |
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97 | (5) |
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2.7 Periodic orbits and resonance |
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102 | (6) |
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108 | (6) |
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2.9 Two-dimensional attractors |
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114 | (5) |
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119 | (4) |
| Bibliography |
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123 | |
Dr Mike Jeffrey is a Senior Lecturer at the University of Bristol in the United Kingdom.
Paul Glendinning is a Professor of Applied Mathematics at the University of Manchester in the United Kingdom.
