Description
Book SynopsisProvides a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book can be covered independently in one semester each or combined together into a year long course.
Trade ReviewThis is an appealing and readable introduction to dynamical systems that would serve the needs of a variety of courses or support self-study." - William J. Satzer,
MAA ReviewsTable of Contents
- 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
