Finiteness of integrable n-dimensional homogeneous polynomial potentials
Copyright policy )Finiteness of integrable n-dimensional homogeneous polynomial potentials
We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is integrable. We also explain how to find explicit forms of these integrable potentials for small $k$.
- Grenoble Alpes University France
- University of Grenoble France
- Joseph Fourier University France
- Nicolaus Copernicus University Poland
- Institut Fourier (Université Grenoble-Alpes) France
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, hypergeometric equation, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, integrability, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Hamiltonian systems, Exactly Solvable and Integrable Systems (nlin.SI), Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria), Kovalevskaya exponents
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, hypergeometric equation, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, integrability, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Hamiltonian systems, Exactly Solvable and Integrable Systems (nlin.SI), Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria), Kovalevskaya exponents
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