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Symmetric periodic orbits and uniruled real Liouville domains
Frauenfelder, U.,van Koert, O. Springer Science + Business Media 2016 Chinese annals of mathematics. Ser. B Vol.37 No.4
<P>A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.</P>
THE GRADIENT FLOW EQUATION OF RABINOWITZ ACTION FUNCTIONAL IN A SYMPLECTIZATION
Urs Frauenfelder 대한수학회 2023 대한수학회지 Vol.60 No.2
Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.
MORSE HOMOLOGY ON NONCOMPACT MANIFOLDS
Cieliebak, Kai,Frauenfelder, Urs Korean Mathematical Society 2011 대한수학회지 Vol.48 No.4
Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a bidirect system. We discuss in this note the relation between these different limits.
MORSE HOMOLOGY ON NONCOMPACT MANIFOLDS
Kai Cieliebak,Urs Frauenfelder 대한수학회 2011 대한수학회지 Vol.48 No.4
Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a bidirect system. We discuss in this note the relation between these different limits.