Year: 1988
Type: article
Abstract: We consider a one parameter family of flows generated by x ˙ = f ( x , λ ) \dot x = f\left ( {x,\lambda } \right ) , where λ ∈ [ 0 , 1 ] \lambda \in \left [ {0,1} \right ] . We, also, assume that there exists an isolated invariant set, S S , which continues across the interval [ 0 , 1 ] \left [ {0,1} \right ] , and that we know the connection matrices for x ˙ = f ( x , 1 ) \dot x = f\left ( {x,1} \right ) and x ˙ = f ( x , 0 ) \dot x = f\left ( {x,0} \right ) . We then give conditions under which a Morse decomposition of S S cannot continue across [ 0 , 1 ] \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.
Author: Konstantin Mischaikow
Institution: Brown University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Award: G3919476097
OpenAlex ID: W2072830509