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Vector Fields and Dynamical Systems

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Book Id: WPLBN0000676041
Format Type: PDF eBook
File Size: 892.30 KB
Reproduction Date: 2005
Full Text

Title: Vector Fields and Dynamical Systems  
Language: English
Subject: Science., Mathematics, Logic
Publication Date:

Mathematics document containing theorems and formulas.

Excerpt: This chapter studies vector fields and the dynamical systems they determine. The ensuing chapters will study the related topics of tensors and differential forms. A basic operation introduced in this chapter is the Lie derivative of a function or a vector field. It is introduced in two different ways, algebraically as a type of directional derivative and dynamically as a rate of change along a flow. The Lie derivative formula asserts the equivalence of these two definitions. The Lie derivative is a basic operation used extensively in differential geometry, general relativity, Hamiltonian mechanics, and continuum mechanics.


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