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Qualitative Theory of Differential Equations - Mathematics

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Description

Qualitative Theory of Differential Equations explores subriemannian geometries, also known as Carnot-Caratheodory geometries, which emerge as limits of Riemannian geometries and arise in physical phenomena involving geometric phases and holonomy. This mathematical analysis text examines how a subriemannian geometry consists of a manifold endowed with a distribution, described as a k-plane field or subbundle of the tangent bundle, called horizontal, together with an inner product on that distribution. When k equals n, the dimension of the manifold, the geometry becomes the usual Riemannian geometry. The book provides rigorous mathematical treatment of distance definitions and geometric properties within subriemannian frameworks.

Key Features

Qualitative Theory of Differential Equations covers subriemannian geometry concepts with mathematical rigour suitable for advanced mathematics students.

The text explores Carnot-Caratheodory geometries and their role as limits of Riemannian geometries in differential equations.

Published by American Mathematical Society, ensuring academic credibility and comprehensive treatment of mathematical analysis topics.

The book examines geometric phases, holonomy phenomena, and manifold theory essential to understanding differential equation behaviour.

Features detailed exploration of k-plane fields, tangent bundles, and inner product structures in differential geometry applications.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
06 September 2007
Listed Since
20 June 2007

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