This article is cited in 7 papers

On separatrix splitting of some quadratic area-preserving maps of the plane

V. L. Chernov

Faculty of Physics, Department of Mathematical Physics, Saint-Petersburg State University, Ulianovskaya str. 1/1, Petrodvorets, 198904, Saint-Petersburg, Russia

Abstract: Hamiltonian dynamical systems are considered in this article. They come from iterations of area-preserving quadratic maps of the plain. Stable and unstable invariant curves of the map $QM(u,v)=(v+u+u^2,v+u^2)$ passing across the origin are presented in the form of the Laplace's integrals from the same function but along the different contours. Also an asymptotic of their difference calculated splitting of the map $HM(X,Y)=(Y+X+\varepsilon X(1-X),Y+\varepsilon X(1-X))$. An asimptotic formula is given for a homoclinic invariant as $\varepsilon \to 0$, but it did not prove rigorously.

MSC: 58F05

Received: 15.01.1998

Language: English

DOI: 10.1070/RD1998v003n01ABEH000060

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