Sara Di Ruzza

Università degli Studi di Palermo

Analysis of Euler integral in the three–body problem

We present a numerical study of the three–body problem in the planar case through the analysis of the variation of the Euler integral. We reduce the Hamiltonian from 3 to 2 degrees of freedom and discuss in detail the 3–dimensional phase space of two concrete orbits. In particular, we study the variation of the Euler integral function around an orbit which spends much time closely to the saddle point of a manifold where the Euler integral is constant. Moreover, we show the existence of chaos, via symbolic dynamics, in the region close to the saddle point, using covering relations. The work is joint with Gabriella Pinzari.

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Analysis of Euler integral in the three–body problem
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