 00402 Vassili Gelfreich
 Splitting of separatrices near resonant periodic orbit
(1267K, LaTeX 2e)
Oct 12, 00

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We consider an analytic family of areapreserving maps
$F_\varepsilon$ with an elliptic fixed point. We assume that for
$\varepsilon=0$ the fixed point is resonant of an order $n=1,2$ or $3$.
In each of these cases the fixed point can be unstable at the
exact resonance, and close to the exact resonance
there is a hyperbolic periodic orbit. The resonant normal form
is integrable and its separatrices form a small loop.
Separatrices of the map $F_\varepsilon$ are close to the
separatrices of the normal form but can intersect transversally.
Asymptotic formulae for the splitting of separatrices
are provided.
The splitting is exponentially small compared to $\varepsilon$
and can not be detected by Melnikov method.
This problem is equivalent to studying a generic family of
closetoresonant elliptic periodic orbits in an analytic Hamiltonian system
with two degrees of freedom.
 Files:
00402.src(
00402.keywords ,
mp_arc.tex )