Titlebook: Differential Geometry, Differential Equations, and Mathematical Physics; The Wisła 19 Summer Maria Ulan,Eivind Schneider Book 2021 Baltic

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Critical Phenomena in Darcy and Euler Flows of Real Gases,w and flows of inviscid gases described by Euler equations. We explicitly formulate thermodynamics in terms of contact and symplectic geometry and show the link between thermodynamics and measurement theory. The methods provided by the geometrical reformulation of thermodynamics are applied to the a

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Differential Invariants for Flows of Fluids and Gases,iants. This analysis is based on consideration of Riemannian structure naturally associated with Lagrangian manifolds that represent thermodynamic states. This approach radically changes the description of the thermodynamic part of the symmetry algebra as well as the field of differential invariants

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Die Internationale Raumstation ISS,These notes present elementary introduction to tractors based on classical examples, together with glimpses towards modern invariant differential calculus related to vast class of Cartan geometries, the so-called parabolic geometries.

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https://doi.org/10.1007/978-3-531-92619-3In these lectures, I want to illustrate an application of symmetry ideas to integration of differential equations. Basically, we will consider only differential equations of finite type, i.e. equations with finite-dimensional space Sol of (local) solutions. Ordinary differential equations make up one of the main examples of such equations.

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Joachim Schöffel,Raimund KemperThe theory of finite dimensional dynamics is a natural development of the theory of dynamical systems. Dynamics make it possible to find families that depend on a finite number of parameters among all solutions of evolutionary differential equations.

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Notes on Tractor Calculi,These notes present elementary introduction to tractors based on classical examples, together with glimpses towards modern invariant differential calculus related to vast class of Cartan geometries, the so-called parabolic geometries.

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