Math 6104 Infinite dimensional dynamical systems

Description

This course is about the basic theory of infinite dimensional dynamical systems. The contents include the dynamical systems approach to evolution equations; dissipative dynamical systems(limit sets and global attractors, chain transitive sets, uniform persistence); monotone dynamics (attracting order intervals and connecting orbits, global attractivity and convergence, and
subhomogeneous maps); traveling waves and spreading speeds; and applications to population biology.

Prerequisites

Ordinary and partial differential equations, dynamical systems, functional analysis, and point set topology at the undergraduate level.

Textbook

  • X. Zhao, Dynamical Systems in Population Biology, second edition, Springer-Verlag, New York, 2017.

References

  • J. K. Hale, Asymptotic Behavior of Dissipative Systems,
    Amer. Math. Soc., Providence, 1988.
  • H. L. Smith, Monotone Dynamical Systems, An Introduction to the
    Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs 41, Amer. Math. Soc., Providence, RI,1995.

Contact

Mathematics and Statistics

230 Elizabeth Ave, St. John's, NL, CANADA, A1B 3X9

Postal Address: P.O. Box 4200, St. John's, NL, CANADA, A1C 5S7

Tel: (709) 864-8000