Frobenius theorem and invariants for Hamiltonian systems

Details Frobenius theorem and invariants for Hamiltonian systems Frobenius theorem and invariants for Hamiltonian systems

2002-11-17

arxiv.org/abs/math-ph/0211039v1

J. Phys. A: Math. Gen. v. 34 (2001) 1005-1017

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/34/5/306

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem.

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