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arXiv · 1904.12906

Symmetries and hamiltonians of Ince's XXXVIII and XLIX equations

V. C. C. Alves·H. Aratyn·J. F. Gomes·A. H. Zimerman
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Abstract

We discuss symmetries of Hamiltonians of I$_{38}$ and I$_{49}$ equations that appear on Ince's list of fifty second-order differential equations with Painlev\'e property. This study is informed by structure of Weyl symmetries of Painlev\'e P$_{III}$ and mixed Painlev\'e P$_{III-V}$ equations and provides insights into differences between the symmetries of Painlev\'e equations and symmetries of solvable equations on Ince's list.

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V. C. C. Alves, H. Aratyn, J. F. Gomes, A. H. Zimerman. 2019-04-29. Symmetries and hamiltonians of Ince's XXXVIII and XLIX equations. https://doi.org/10.1088/1742-6596/1194/1/012002

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