portada morse theory, gradient flows, concavity and complexity on manifolds with boundary (en Inglés)

morse theory, gradient flows, concavity and complexity on manifolds with boundary (en Inglés)

Formato

Libro Físico

Autor

Gabriel Katz

Editorial

World Scientific Publishing Company

Año

2012

Idioma

Inglés

N° páginas

516

Encuadernación

Tapa Dura

Dimensiones

22.9x15.2x2.9 cm

Peso

0.85 kg.

ISBN

981436875x

ISBN13

9789814368759

Categorías

Cálculo y análisis matemático
Geometría
Topología

morse theory, gradient flows, concavity and complexity on manifolds with boundary (en Inglés)

Gabriel Katz (Autor) · World Scientific Publishing Company · Tapa Dura

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Reseña del libro "morse theory, gradient flows, concavity and complexity on manifolds with boundary (en Inglés)"

This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.