Periodic first integrals for hamiltonian systems of lie type
TLDR
In this article, the existence problem of periodic first integrals for periodic Hamiltonian systems of Lie type was studied and the existence of Poisson algebras of periodic integrals was proved under different criteria based on properties for the Killing form of the adjoint group.Abstract:
In this paper, we study the existence problem of periodic first integrals for periodic Hamiltonian systems of Lie type. From a natural ansatz for time-dependent first integrals, we refer their existence to the existence of periodic solutions for a periodic Euler equation on the Lie algebra associated to the original system. Under different criteria based on properties for the Killing form or on exponential properties for the adjoint group, we prove the existence of Poisson algebras of periodic first integrals for the class of Hamiltonian systems considered. We include an application for a nonlinear oscillator having relevance in some modern physics applications.read more
Citations
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Dirac-Lie systems and Schwarzian equations
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Lie-Hamilton Systems: Theory and Applications
TL;DR: In this article, the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features, called the Lie-Hamilton systems, is discussed. But their results are illustrated by examples of physical and mathematical interest.
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From constants of motion to superposition rules for Lie?Hamilton systems
TL;DR: In this article, it was shown that Lie Hamilton systems are naturally endowed with a Poisson coalgebra structure, which allows us to derive constants of motion and superposition rules in an algebraic way.
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Lie--Hamilton systems: theory and applications
TL;DR: In this paper, the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features, called the Lie-Hamilton systems, is discussed. But their results are illustrated by examples of physical and mathematical interest.
Journal ArticleDOI
From constants of motion to superposition rules for Lie-Hamilton systems
TL;DR: In this paper, it was shown that Lie-Hamilton systems are naturally endowed with a Poisson coalgebra structure, which allows us to derive constants of motion and superposition rules in an algebraic way.
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TL;DR: In this article, the authors propose a model for projective transformation of a projective Gruppe in der Ebene, which is based on the lineare homogene Gruppen.
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Superposition rules, lie theorem, and partial differential equations
TL;DR: In this paper, a rigorous geometric proof of the Lie theorem on nonlinear superposition rules for solutions of nonautonomous ordinary differential equations is given filling in all the gaps present in the existing literature.