Veech, William A. Department of Mathematics, Rice University, Houston, Texas.
- Topological transformation groups
- Classical dynamical systems
- Poincaré recurrence theorem
- Flows on manifolds
- Principle of least action
- Whitney sums
- Hyperbolic structure
- Structural stability
- Anosov's theorem
- Symbolic dynamics
- Ergodic theory
- Ornstein's theorem
- Bernoulli shifts as models
- Minimal transformation groups
- Links to Primary Literature
- Additional Readings
The study and application of topological transformation groups. Topological dynamics originated in the late-nineteenth-century investigations of the qualitative behavior of the solutions to the differential equations of classical mechanics by Henri Poincaré. The emergence of topological dynamics as a mathematical discipline occurred in the twentieth century with an abstract formulation of certain qualitative features of the classical systems by G. D. Birkhoff.
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