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Fractal structures for the Jacobi Hamiltonian of restricted three-body problem
Institution:1. Institut UTINAM, Observatoire des Sciences de l’Univers THETA, CNRS, Université de Franche-Comté, Besançon 25030, France;2. Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, Toulouse 31062, France;1. TEI of Western Macedonia, Kozani, Greece;2. KAIST, Daejeon, South Korea;3. University of Ioannina, Ioannina Gr 451 10, Greece;4. Department of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece;5. Department of Physics, Ben Gurion University, Israel;1. Department of Physics, H.R. Institute of Technology, Ghaziabad 201003, India;2. Astrophysics Research Group, Meerut College, Meerut 250002, India;3. Uttarakhand Space Application Centre, Dehradun 248006, India;4. Department of Physics, MM College, Modinagar, Ghaziabad 201204, India;1. Astronomy Department and Meteorology, Faculty of Science, Al-Azhar University, Cairo, Egypt\n;2. Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt\n;3. Kottamia Center of Scientific Excellence in Astronomy and Space Sciences (KCScE) STDF, ASRT, Cairo, Egypt\n
Abstract:We study the dynamical chaos and integrable motion in the planar circular restricted three-body problem and determine the fractal dimension of the spiral strange repeller set of non-escaping orbits at different values of mass ratio of binary bodies and of Jacobi integral of motion. We find that the spiral fractal structure of the Poincaré section leads to a spiral density distribution of particles remaining in the system. We also show that the initial exponential drop of survival probability with time is followed by the algebraic decay related to the universal algebraic statistics of Poincaré recurrences in generic symplectic maps.
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