Cayley-Sylvester invariants and the Hamilton equations
P.L. Robinson
TL;DR
This paper explores how Cayley-Sylvester invariant theory applies to Hamilton equations derived from cubic and quartic Hamiltonian functions, revealing new insights into their mathematical structure.
Contribution
It introduces a novel connection between invariant theory and Hamiltonian dynamics for higher-degree Hamiltonians.
Findings
Identifies specific invariants for cubic and quartic Hamiltonians.
Provides a framework for analyzing Hamilton equations using invariant theory.
Suggests potential applications in integrability and symmetry analysis.
Abstract
We note implications of the Cayley-Sylvester theory of invariants and covariants for the Hamilton equations generated by cubic and quartic Hamiltonian functions.
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Taxonomy
TopicsNumerical methods for differential equations · Matrix Theory and Algorithms · Control and Stability of Dynamical Systems