Work

Asymptotically Autonomous Semiflows: Chain Recurrence and Lyapunov Functions

Year: 1995

Type: article

Abstract: From the work of C. Conley, it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set. Here, we improve a result of L. Markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow. In the special case that there is a Lyapunov function for the limiting semiflow, sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the Lyapunov function.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/s0002-9947-1995-1290727-7

Authors: Konstantin Mischaikow, Hal Smith, Horst R. Thieme

Institutions: Georgia Institute of Technology, Arizona State University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: Mathematical Sciences: Stability, Oscillations, and Persistence in Differential Equation Models for Structured Populations., Mathematical Sciences: Dynamical Systems in Biology, Mathematical Sciences: Conley Index Theory and Its Applications