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Differential geometry. Global analysis --- Singularities (Mathematics) --- Manifolds (Mathematics) --- Singularités (Mathématiques) --- Variétés (Mathématiques) --- Differentiable mappings --- SINGULARITIES (Mathematics) --- 515.16 --- Topology of manifolds --- Differentiable mappings. --- Manifolds (Mathematics). --- Singularities (Mathematics). --- 515.16 Topology of manifolds --- Singularités (Mathématiques) --- Variétés (Mathématiques) --- Geometry, Algebraic --- Geometry, Differential --- Topology --- Differentiable maps --- Mappings, Differentiable --- Differential topology --- Mappings (Mathematics) --- Applications différentiables --- Singularités (mathématiques) --- Topologie différentielle --- Applications différentiables --- Singularités (mathématiques) --- Topologie différentielle --- Analyse sur une variété

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Philosophy of nature --- Philosophy of science

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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. This 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.

Symmetry --- Bifurcation theory --- Chaotic behavior in systems --- Physical Sciences & Mathematics --- Sciences - General --- Symmetry. --- Bifurcation theory. --- Chaotic behavior in systems. --- Harmonic analysis. Fourier analysis --- Ordered algebraic structures --- Mathematical physics --- Applied mathematics. --- Engineering mathematics. --- Dynamics. --- Ergodic theory. --- Functions of complex variables. --- Statistical physics. --- Dynamical systems. --- Mathematical and Computational Engineering. --- Applications of Mathematics. --- Dynamical Systems and Ergodic Theory. --- Functions of a Complex Variable. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Complex variables --- Elliptic functions --- Functions of real variables --- Ergodic transformations --- Continuous groups --- Measure theory --- Transformations (Mathematics) --- Engineering --- Engineering analysis --- Mathematical analysis --- Statistical methods

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Algebras, Linear --- Differential equations --- Algèbre linéaire --- Équations différentielles --- Data processing. --- Informatique. --- Algèbre linéaire --- Équations différentielles

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Symmetry