Geodesic
Methods of high-accuracy integration and effectivity of calculus
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2009), pp. 153-161

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The paper deals with a transition to chaos in the phase-plane portrait of a restricted problem of rotation of a rigid body with a fixed point. Two interrelated mechanisms responsible for chaotisation have been indicated: 1) growth of the homoclinic structure and 2) development of cascades of period doubling bifurcations. On the zero level of the integral of areas, an adiabatic behavior of the system (as the energy tends to zero) has been noticed. Meander tori induced by the breakdown of the torsion property of the mapping have been found.
Keywords: motion of a rigid body
Mots-clés : phase-plane portrait, mechanism of chaotisation, bifurcations. 
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     author = {A. A. Kilin},
     title = {Methods of high-accuracy integration and effectivity of calculus},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {153--161},
     publisher = {mathdoc},
     number = {1},
     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2009_1_a6/}
}
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A. A. Kilin. Methods of high-accuracy integration and effectivity of calculus. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2009), pp. 153-161. http://geodesic.mathdoc.fr/item/VUU_2009_1_a6/