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KIAM Preprint Ļ 34, Moscow, 2011
Authors: Batkhin A.B.
Symbolic dynamics and generating planar periodic orbits of the Hillís problem
Abstract:
We consider the planar circular Hillís problem and its limiting case called the intermediate H´enon problem. The Hillís problem is a singular perturbation of the former. There is a countable set of generating arcĖsolutions each of them is defined by the condition of passing through the singular point of the Hillís problem. It is shown that each arcĖsolution has its own invariant manifold defined by the additional first integral of motion of the intermediate H´enon problem. The generating solutions of families of periodic orbits of the Hillís problem are built from the arc-solutions like words are composed from letters. The set of all the right composed ďwordsĒ defines the symbolic dynamics of the system.
Publication language: russian,  pages: 31
Research direction:
Mathematical problems and theory of numerical methods
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  • Batkhin A.B.