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Publisher:

World Scientific

Publication Date:

2004

Number of Pages:

502

Format:

Hardcover

Series:

Interdisciplinary Mathematical Sciences 1

Price:

88.00

ISBN:

981-256-028-9

Category:

Monograph

[Reviewed by , on ]

William J. Satzer

05/28/2005

The initial chapter introduces autonomous equations, describes several different versions of what "dissipative" can mean, and establishes when they are and are not equivalent. The second chapter begins the discussion of non-autonomous dissipative systems. Successive chapters explore special aspects and settings for non-autonomous dissipative systems: the analytic context, Lyapunov function methods, structure of global attractors, and triangle maps. One chapter focuses on global attractors for non-autonomous Navier-Stokes equations.

This is an extremely dense text that would be very challenging for anyone but experts in the field. The thread connecting individual chapters is pretty thin so it is difficult to understand how individual topics relate to each other. The index is sparse and it is very difficult to trace back to find definitions, for example. The writing is usually clear enough locally, in individual sections, but there are occasional non-idiomatic or ungrammatical phrases that are confusing. Overall, this book needs some serious editing and a far better index.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

# Autonomous Dynamical Systems

# Non-Autonomous Dissipative Dynamical Systems

# Analytic Dissipative Systems

# The Structure of the Levinson Centre of System with the Condition of the Hyperbolicity

# Method of Lyapunov Functions

# Dissipativity of Some Classes of Equations

# Upper Semi-Continuity of Attractors

# The Relationship between Pullback, Forward and Global Attractors

# Pullback Attractors of C-Analytic Systems

# Pullback Attractors Under Discretization

# Global Attractors of Non-Autonomous Navier-Stokes Equations

# Global Attractors of V-Monotone Dynamical Systems

# Linear Almost Periodic Dynamical Systems

# Triangular Maps.

# Non-Autonomous Dissipative Dynamical Systems

# Analytic Dissipative Systems

# The Structure of the Levinson Centre of System with the Condition of the Hyperbolicity

# Method of Lyapunov Functions

# Dissipativity of Some Classes of Equations

# Upper Semi-Continuity of Attractors

# The Relationship between Pullback, Forward and Global Attractors

# Pullback Attractors of C-Analytic Systems

# Pullback Attractors Under Discretization

# Global Attractors of Non-Autonomous Navier-Stokes Equations

# Global Attractors of V-Monotone Dynamical Systems

# Linear Almost Periodic Dynamical Systems

# Triangular Maps.

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