Non-Integrability Criterion of Hamiltonian Systems based on Ziglin’s Theorem and its Relation to the Singular Point Analysis
After two examples of the singular point analysis, a sufficient condition (criterion) for the non-existence of an additional analytic integral is given for n-degree-of-freedom Hamiltonian systems with a homogeneous potential, which justifies the validity of the singular point analysis. This criterion is based on Ziglin’s theorem, which will be reviewed extensively from the basic ideas.
KeywordsPeriodic Solution Hamiltonian System Characteristic Exponent Monodromy Matrix Jacobi Elliptic Function
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