An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition

ISBN-13: 9780821891353 / Angielski / Twarda / 2013 / 733 str.

R Clark Robinson

Opis

This book gives an introduction into the ideas of dynamical systems. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit. It is divided into two parts which can be read in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function. For professionals with a strong mathematics background.

Spis treści

• Historical prologue
• Part I. Systems of nonlinear differential equations
• Geometric approach to differential equations
• Linear systems
• The flow: Solutions of nonlinear equations
• Phase portraits with emphasis on fixed points
• Phase portraits using Scalar functions
• Periodic orbits
• Chaotic attractors
• Part II. Iteration of functions
• Iteration of functions as dynamics
• Periodic points of one-dimensional maps
• Itineraries for one-dimensional maps
• Invariant sets for one-dimensional maps
• Periodic points of higher dimensional maps
• Invariant sets for higher dimensional maps
• Fractals
• Background and terminology
• Generic properties Bibliography