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On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter

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In this paper, we have found necessary and sufficient conditions under which two Abel equations with coefficients depending on a control parameter are locally equivalent with respect to the same pseudogroup of feedback transformations. These conditions are formulated in terms of differential invariants.

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Authors and Affiliations

  1. Kazan’ (Volga Region) Federal University, Kazan’, Russia

    V. V. Shurygin Jr.

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  1. V. V. Shurygin Jr.
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Correspondence to V. V. Shurygin Jr..

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.

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Shurygin, V.V. On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter. J Math Sci 248, 505–510 (2020). https://doi.org/10.1007/s10958-020-04891-1

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  • DOI: https://doi.org/10.1007/s10958-020-04891-1

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