Differential Dynamical Systems
Jan 2007 · Mathematical Modeling and Computation Kitabu cha 14 · SIAM
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Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines traditional teaching on ordinary differential equations with an introduction to the more modern theory of dynamical systems, placing this theory in the context of applications to physics, biology, chemistry, and engineering. Beginning with linear systems, including matrix algebra, the focus then shifts to foundational material on non-linear differential equations, drawing heavily on the contraction mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts - flow, chaos, invariant manifolds, bifurcation, etc. An appendix provides simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems. For senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with differential equations and linear algebra and have had some exposure to advanced calculus.
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James D. Meiss is a Professor in the Department of Applied Mathematics at the University of Colorado at Boulder. He is a fellow of the American Physical Society. His work in dynamical systems focuses on Hamiltonian dynamics, the transition to chaos, and the theory of transport.
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