Existence of generalized homoclinic orbits for one parameter families of flows
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- by Konstantin Mischaikow PDF
- Proc. Amer. Math. Soc. 103 (1988), 59-68 Request permission
Abstract:
We consider a one parameter family of flows generated by $\dot x = f\left ( {x,\lambda } \right )$, where $\lambda \in \left [ {0,1} \right ]$. We, also, assume that there exists an isolated invariant set, $S$, which continues across the interval $\left [ {0,1} \right ]$, and that we know the connection matrices for $\dot x = f\left ( {x,1} \right )$ and $\dot x = f\left ( {x,0} \right )$. We then give conditions under which a Morse decomposition of $S$ cannot continue across $\left [ {0,1} \right ]$. Furthermore, using the language of chain recurrence we define a generalized homoclinic orbit and give conditions under which such objects exist.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 59-68
- MSC: Primary 58F14
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938645-7
- MathSciNet review: 938645