Inverse Jacobi multipliers
By L. R. Berrone, Héctor Giacomini. 2003
63 citations recorded by the source corpus.
Inverse Jacobi multipliers are a natural generalization of inverse integrating factors ton-dimensional dynamical systems. In this paper, the corresponding theory is developed from its beginning in the formal methods of integration of ordinary differential equations and the “last multiplier” of K. G. Jacobi. We explore to what extent the nice properties of the vanishing set of inverse integrating factors are preserved in then -dimensional case. In particular, vanishing on limit cycles (in restricted sense) of an inverse Jacobi multiplier is proved by resorting to integral invariants. Extensions of known constructions of inverse integrating factors by means of power series, local Lie Groups and algebraic solutions are provided for inverse Jacobi multipliers as well as a suitable generalization of the concept to systems with discontinuous right-hand side.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7a1064beaa9cbf8b7e899e6e2f31af8f7238f924
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- A Survey on the Inverse Integrating Factor (2009, methodology): “Theorem 61 [4] Let V be a Jacobi inverse multiplier defined in a neighborhood of a limit cycle γ of the vector field X .”
- Jacobi Last Multiplier and Lie Symmetries: A Novel Application of an Old Relationship (2005, background): “... a Lagrangian formulation for systems of second-order ordinary differential equations ([58], [38], [29]); to searching for steady compressible flows of perfect gases [51] or applying it to the statistical mechanics of dissipative systems [14]; from identifying the time-dependent probability densi”