Displaying similar documents to “Some stability questions concerning caustics for different propagation laws.”

Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

Wladimir G. Boskoff, Bogdan D. Suceavă (2008)

Czechoslovak Mathematical Journal

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In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian's metrization procedure can be relaxed. Then, we prove that Barbilian's metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.

Remarks on Riemannian Thermodynamics

Luigi G. Napolitano, Carlo Albanese (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The postulates of macroscopic thermodynamics give us the possibility to endow the set of thermodynamic states with the structure of a riemannian manifold. Two alternatives are available: the first one is to introduce on the set of thermodynamic equilibrium states a metric induced by an embedding metric space (extrinsic approach), the second one is to introduce the stability metric (intrinsic approach). Between the two choices the second one looks more promising on the basis of its capability...

Catastrophes and partial differential equations

John Guckenheimer (1973)

Annales de l'institut Fourier

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This paper outlines the manner in which Thom’s theory of catastrophes fits into the Hamilton-Jacobi theory of partial differential equations. The representation of solutions of a first order partial differential equation as lagrangian manifolds allows one to study the local structure of their singularities. The structure of generic singularities is closely related to Thom’s concept of the elementary catastrophe associated to a singularity. Three concepts of the stability of a singularity...