Geometrical structures of higher-order dynamical systems and field theories
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In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian function/density, or a Hamiltonian that admits Lagrangian counterpart. These geometric frameworks are used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.
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Cited by 2 Pith papers
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Gauge Symmetries, Contact Reduction, and Singular Field Theories
Scale symmetry reduction applied to singular Lagrangians via De-Donder-Weyl formalism yields equivalent frictional dynamics for particles and fields, with applications to general relativity.
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Constrained Symplectic and Contact Hamiltonian Systems: A Review
A review presents the geometry of pre-symplectic and pre-contact manifolds and develops constraint algorithms for admissible phase space in Hamiltonian systems with degeneracies.
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