Topological Invariants of Plane Curves and Caustics: 005

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9780821803080: Topological Invariants of Plane Curves and Caustics: 005

This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions.

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Arnold, V. I.
ISBN 10: 0821803085 ISBN 13: 9780821803080
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218030800000000

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V. I. Arnold
Editore: American Mathematical Society, United States (1994)
ISBN 10: 0821803085 ISBN 13: 9780821803080
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Descrizione libro American Mathematical Society, United States, 1994. Paperback. Condizione libro: New. 244 x 170 mm. Language: English . Brand New Book. This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces.Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions. Codice libro della libreria AAN9780821803080

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V. I. Arnold
Editore: American Mathematical Society, United States (1994)
ISBN 10: 0821803085 ISBN 13: 9780821803080
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Descrizione libro American Mathematical Society, United States, 1994. Paperback. Condizione libro: New. 244 x 170 mm. Language: English . Brand New Book. This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces.Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions. Codice libro della libreria AAN9780821803080

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Descrizione libro American Mathematical Society. Paperback. Condizione libro: new. BRAND NEW, Topological Invariants of Plane Curves and Caustics, V. I. Arnold, This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces.Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions. Codice libro della libreria B9780821803080

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V. I. Arnold
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ISBN 10: 0821803085 ISBN 13: 9780821803080
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Descrizione libro American Mathematical Society, 1994. Paperback. Condizione libro: New. Brand new. We distribute directly for the publisher. This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions. Codice libro della libreria 1007090007

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V. I. Arnold
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Descrizione libro American Mathematical Society, 1994. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria CE-9780821803080

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Arnold, V. I.
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Descrizione libro Amer Mathematical Society, 1994. Paperback. Condizione libro: Brand New. 60 pages. 10.00x7.00x0.25 inches. In Stock. Codice libro della libreria __0821803085

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V. I. Arnold
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Descrizione libro American Mathematical Society, 1994. Paperback. Condizione libro: New. Codice libro della libreria DADAX0821803085

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V. I. Arnold
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Descrizione libro Condizione libro: Brand New. Book Condition: Brand New. Codice libro della libreria 97808218030801.0

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V. I. Arnold
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Descrizione libro American Mathematical Society, 1994. Paperback. Condizione libro: New. Codice libro della libreria P110821803085

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