A Time scales Noether's theorem
Baptiste Anerot, Jacky Cresson, Fr\'ed\'eric Pierret
TL;DR
This paper extends Noether's theorem to the calculus on time scales, unifying continuous and discrete cases, and corrects previous inaccuracies in the literature.
Contribution
It provides a generalized version of Noether's theorem applicable to time scales, bridging continuous and discrete frameworks.
Findings
Unified Noether's theorem on time scales established.
Corrects previous errors in the discrete case.
Shows the relation between symmetries and conservation laws on time scales.
Abstract
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of Bartosiewicz and Torres in \cite{BT}.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Stability and Controllability of Differential Equations · advanced mathematical theories