Riemann geometry in theory of the first order systems of equations
Valery Dryuma (Imi as RM)
TL;DR
This paper explores the application of Riemann geometry to analyze first-order nonlinear differential systems, including quadratic and Lorenz systems, providing a geometric framework for their study.
Contribution
It introduces a Riemann extension approach to analyze properties of nonlinear first-order systems, expanding geometric methods in differential equations.
Findings
Detailed investigation of quadratic planar systems
Analysis of Lorenz system within Riemann geometric framework
Insights into nonlinear system properties through geometry
Abstract
Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz system of equations are investigated in detail.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic and Geometric Analysis · advanced mathematical theories