Ebook: The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space

Pattern formation in physical systems is one of the major research frontiers of mathematics. A central theme of this book is that many instances of pattern formation can be understood within a single framework: symmetry.

The book applies symmetry methods to increasingly complex kinds of dynamic behavior: equilibria, period-doubling, time-periodic states, homoclinic and heteroclinic orbits, and chaos. Examples are drawn from both ODEs and PDEs. In each case the type of dynamical behavior being studied is motivated through applications, drawn from a wide variety of scientific disciplines ranging from theoretical physics to evolutionary biology. An extensive bibliography is provided.

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Content:
Front Matter....Pages i-xvii
Steady-State Bifurcation....Pages 1-31
Linear Stability....Pages 33-57
Time Periodicity and Spatio-Temporal Symmetry....Pages 59-86
Hopf Bifurcation with Symmetry....Pages 87-122
Steady-State Bifurcations in Euclidean Equivariant Systems....Pages 123-159
Bifurcation From Group Orbits....Pages 161-199
Hidden Symmetry and Genericity....Pages 201-220
Heteroclinic Cycles....Pages 221-240
Symmetric Chaos....Pages 241-274
Periodic Solutions of Symmetric Hamiltonian Systems....Pages 275-300
Back Matter....Pages 301-325

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Content:
Front Matter....Pages i-xvii
Steady-State Bifurcation....Pages 1-31
Linear Stability....Pages 33-57
Time Periodicity and Spatio-Temporal Symmetry....Pages 59-86
Hopf Bifurcation with Symmetry....Pages 87-122
Steady-State Bifurcations in Euclidean Equivariant Systems....Pages 123-159
Bifurcation From Group Orbits....Pages 161-199
Hidden Symmetry and Genericity....Pages 201-220
Heteroclinic Cycles....Pages 221-240
Symmetric Chaos....Pages 241-274
Periodic Solutions of Symmetric Hamiltonian Systems....Pages 275-300
Back Matter....Pages 301-325
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