117 research outputs found
Effective algorithm of analysis of integrability via the Ziglin's method
In this paper we continue the description of the possibilities to use
numerical simulations for mathematically rigorous computer assisted analysis of
integrability of dynamical systems. We sketch some of the algebraic methods of
studying the integrability and present a constructive algorithm issued from the
Ziglin's approach. We provide some examples of successful applications of the
constructed algorithm to physical systems.Comment: a figure added, version accepted to JDC
The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach
A symplectic theory approach is devised for solving the problem of
algebraic-analytical construction of integral submanifold imbeddings for
integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on
canonically symplectic phase spaces
- …