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The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos

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  • We consider a special situation of the Hess-Appelrot case of the Euler-Poisson system which describes the dynamics of a rigid body about a fixed point. One has an equilibrium point of saddle type with coinciding stable and unstable invariant 2-dimensional separatrices. We show rigorously that, after a suitable perturbation of the Hess-Appelrot case, the separatrix connection is split such that only finite number of 1-dimensional homoclinic trajectories remain and that such situation leads to a chaotic dynamics with positive entropy and to the non-existence of any additional first integral.

    Mathematics Subject Classification: Primary: 05C38, 15A15; Secondary: 05A15, 15A18.


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  • Figure 1.  Ovals of elliptic curves

    Figure 2.  The scheme of the separatrix connection and of the sections

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