【摘 要】
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The course is a short introduction to some aspects of the simplest non-integrable three body problem whos study goes back to the seminal works of Hill,Poinc
【机 构】
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ParisⅦandIMCCE,France
【出 处】
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Workshop on Symplectic dynamics and Hamiltonian dynamics(辛动力
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The course is a short introduction to some aspects of the simplest non-integrable three body problem whos study goes back to the seminal works of Hill,Poincar′e and Birkhoff.After Goursat(or Levi Civita)regularization we are led to study a conservative twist map of an annulus whose boundaries are the so-called Hills solutions.We shall show in particular the existence of "quasi-collision solutions" that is of collision-free solutions which come arbitrarily close to collisions.In the phase space,such solutions belong to KAM invariant tori of the regularized system.The main references are [Co,CL].The extensions to the full three-body problem of the existence of quasi-collision solutions,is done in [F,Z].The works of Poincar′e on the restricted problem are described in [C].
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