Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T08:27:56.528Z Has data issue: false hasContentIssue false
  • English
  • Français

Transition systems

Published online by Cambridge University Press:  14 November 2011

Konstantin Mischaikow
Konstantin Mischaikow
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A
Get access Rights & Permissions [Opens in a new window]

Synopsis

The concept of a transition system is extended to a parametrised family of differential equations

where x ∊ ℝn and λ ∊ Λ = [0, l]m, an m-cube. Furthermore, algebraic formulae for comparing connection matrices at the various parameter values are obtained. Finally, several applications of these techniques are indicated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 1-2 , 1989 , pp. 155 - 175
Copyright
Copyright © Royal Society of Edinburgh 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Conley, C. C.. Isolated Invariant Sets and the Morse Index. CMBS Regional Conf. Ser. in Math. Vol. 38 (Providence: American Mathematical Society, 1978).Google Scholar
2.Dold, A.. Lectures on Algebraic Topology (Berlin: Springer, 1972).CrossRefGoogle Scholar
3.Franzosa, R.. The connection matrix theory for Morse decompositions (preprint, 1986).Google Scholar
4.Mischaikow, K.. Classification of traveling wave solutions of reaction diffusion systems (LCDS report 86-5).Google Scholar
5.Mischaikow, K.. Existence of generalized homoclinic orbits for one parameter families of flows. Proc. Amer. Math. Soc. 103 (1988), 59–68.Google Scholar
6.McCord, C. and Mischaikow, K.. Connected simple systems and connection matrices (in prep.).Google Scholar
7.Reineck, J.. Connecting orbits in one-parameter families of flows. Ergodic Theory Dynamical Systems 8 (1988), 359–374.Google Scholar
8.Salamon, D.. Connected simple systems and the Conley index of isolated invariant sets. Trans. Amer. Math. Soc. 29 (1985), 1–41.CrossRefGoogle Scholar
9.Smoller, J.. Shock Waves and Reaction Diffusion Equations (New York: Springer, 1983).CrossRefGoogle Scholar