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Group theory. --- Poincaré series. --- Harmonic oscillators. --- Hadrons.
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Poincaré series --- Representations of groups --- Symmetry (Physics)
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Poincaré series. --- Poincaré, Séries de. --- Développements asymptotiques. --- Asymptotic expansions --- Automorphic functions --- Fonctions automorphes.
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Poincaré duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay's dual systems in the study of irreducible ideals in polynomial algebras. These two ideas are tied together using basic commutative algebra involving Gorenstein algebras. Steenrod operations also originated in algebraic topology, but may best be viewed as a means of encoding the information often hidden behind the Frobenius map in characteristic p<>0. They provide a noncommutative tool to study commutative algebras over a Galois field. In this Tract the authors skilfully bring together these ideas and apply them to problems in invariant theory. A number of remarkable and unexpected interdisciplinary connections are revealed that will interest researchers in the areas of commutative algebra, invariant theory or algebraic topology.
Duality theory (Mathematics) --- Steenrod algebra --- Poincaré series --- Poincaré series. --- Steenrod algebra. --- Algebra, Steenrod --- Algebraic topology --- Algebra --- Mathematical analysis --- Topology --- Series, Poincaré --- Poincare series.
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Group theory. --- Finite groups --- Lie groups --- Poincare series --- Representations of groups --- Finite groups --- Lie groups --- Poincare series --- Representations of groups
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This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the bo
Fractals. --- Poincaré series. --- Series, Poincaré --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Poincare series.
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Poincaré series. --- Representations of groups. --- Symmetry (Physics) --- Poincaré, Séries de --- Représentations de groupes --- Symétrie (physique) --- Poincaré, Séries de --- Représentations de groupes --- Symétrie (physique)
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Field theory (Physics) --- Poincaré series. --- Quantum theory --- Symmetry (Physics). --- Mathematics. --- Mathematics.
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