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\Large \bf
 Bifurcation analyses of capture at the resonance rotation in
     celestial mechanics
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\large  \bf
Alexander V.Gusev and Olga A.Salangina$^\dagger$
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Kazan State University, 18, Lenin str., Kazan, 420008, Russia\\
$^\dagger$ Kazan Physical-Technical Institute, 10/7, Sibirskij str.,
Kazan, 420029, Russia \\
e-mail: gusev@astro.kazan.su \ olgas@open.ksu.ras.ru
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The dynamical picture of distribution matter in Solar system
is testified about a strongly marked tendency in a resonance structure.
The motions of Moon, Mercury, Pluton, Haron, some satellites of Saturn,
Jupiter, Mars  are the resonances.
Some rotations of artificial satellites are presented a resonance too.
The discovery of resonance motion of two celestial bodies
in planet system of solar type around millisecond radiopulsar
PSR B1257+12 is fantastic.

  At the present report for the plane motion we are completely
analyzing the two differential equations systems of  capture
of celestial bodies at the resonance rotation with
action of tidal torques only and with common action
of gravitational and tidal torques by qualitative analysis and
bifurcation theory of dynamical systems.

The analyses of the phase portraits of one-, two-, three-parameter dynamical
systems  and  the bifurcation space of parameters confirm
the gravitational capture. The separations of
parameter spaces of dynamical system by bifurcation surfaces
are obtained.
The gallery  15 (with action of tidal torques) and 79
(with action  of gravitational and tidal torques) phase
portraits of  capture confirms and extends the known
scenario of global evolution celestial bodies.

 Among the bifurcations being investigated we meet the typical
catastrophes of Arnold-Thome from A class, which are
illustrated a structural stability of the gravitational
capture phenomenon at the resonance rotation.

 The present results may be used for investigations
 the rotation of small celestial bodies and satellites.

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