Geodesic
To geometric aspects of infinite-dimensional dynamical systems
Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 163-172

Voir la notice de l'article provenant de la source Math-Net.Ru

The main goal of the work is to construct analogues of Christoffel symbols for infinite-dimensional systems and on this basis to obtain geodesic equations for such systems. These analogies are of particular interest in terms of identifying the relationship between the dynamics of systems with an infinite number of degrees of freedom and Riemannian geometry, as well as geometry defined by the pseudo-Riemannian metric.
Keywords: Christoffel symbols, covariant derivative, geodesic. 
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     title = {To geometric aspects of infinite-dimensional dynamical systems},
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V. M. Savchin. To geometric aspects of infinite-dimensional dynamical systems. Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 163-172. http://geodesic.mathdoc.fr/item/CMFD_2024_70_1_a9/