Singularities of implicit differential systems and their integrability
Takuo Fukuda, Stanisław Janeczko (2004)
Banach Center Publications
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Displaying similar documents to “Lagrangian singularities of invariant tori of hamiltonian systems with two degrees of freedom.”
Singularities of implicit differential systems and their integrability
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On singularities of Hamiltonian mappings
Takuo Fukuda, Stanisław Janeczko (2008)
Banach Center Publications
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The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated. ...
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Dragt, Alex J. (1997)
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Albu, I. D., Opriş, D. (1999)
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E. Zenhder (1975)
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Gauge-independent Hamiltonian reduction of constrained systems.
Muslih, S.I. (2002)
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A simple proof of the non-integrability of the first and the second Painlevé equations
Henryk Żołądek (2011)
Banach Center Publications
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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.