TITLE:
Using normal forms to study Oterma's transition in the Planar RTBP

AUTHORS:
Gladston Duarte^(1,2) and Angel Jorba(1)
(1) Departament de Matematiques i Informatica,
    Universitat de Barcelona (UB) and
    Barcelona Graduate School of Mathematics (BGSMath)
    Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain.
(2) Faculty of Applied Mathematics,
   AGH University of Science and Technology
   Aleja Adama Mickiewicza 30, 30-059, Krakow, Poland.

E-mails: gladston@maia.ub.es, duarteg@agh.edu.pl, angel@maia.ub.es

ABSTRACT:
Comet 39P/Oterma is known to make fast transitions from an
heliocentric orbit outside the orbit of Jupiter to an heliocentric
orbit inside that of Jupiter and vice versa. In this note the dynamics
of Oterma is quantitatively studied via an explicit computation of
high order Birkhoff normal forms at the points $L_1$ and $L_2$ of the
Planar Restricted Three-Body Problem. Previous works~\cite{KoonLMR01}
have shown the existence of heteroclinic connections between the
neigbourhood of $L_1$ and $L_2$ which provide paths for this
transition. Here we combine real data on the motion of Oterma with
normal forms to compute the invariant objects that are responsible
for this transition.