Bifurcations of Critical Orbits of SO(2)-invariant Fredholm Functionals at Critical Points with Double Resonances

Autor:	Yu. I. Sapronov, E.V. Derunova
Rok vydání:	2015
Předmět:	Cycle resonance Lyapunov-Schmidt method bifurcation circular symmetry
DOI:	10.5281/zenodo.7673878
Popis:	In this paper we consider the problem of bifurcation of extremalsof SO(2)-invariant (i.e., with circular symmetry) Fredholm functionalnear a steady-state point with a double-resonance (i.e., with two independentresonance relations). The main method of investigation is avariational modification of the Lyapunov-Schmidt reduction. It allowsus to find a normal form of key functions of functionals. J. Mather’scondition on a finite determinacy of a smooth map germ gives a simplerrepresentation of the key function. Further bifurcational analysisof branching extremals reduces the problem to analysis of boundary andcorner singularities via the secondary reduction.
Databáze:	OpenAIRE
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