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This is a Quantitative Study study.

October 18, 2025

Rigidity theorem for the equation of characteristics of a second-order linear equation of mixed type on a plane at a point where the coefficients are zero

Key Points

The rigidity theorem establishes a link between formal and analytical equivalence for binary differential equations.
It specifically applies to degenerate singular points where the coefficients are zero, leading to a strong conclusion on equivalence.
The equations involve analytic functions around the point (0,0), highlighting their significance in the theory.
This work is grounded in a robust mathematical framework, supported by a substantial bibliography of 36 titles.

Abstract

Binary differential equations (that is, equations of the form a (x, y) dy²+2b (x, y) dx dy+c (x, y) dx²=0, where the coefficients a, b and c are analytic functions in a neighbourhood of the point (0, 0) ) are considered. A rigidity theorem is proved for degenerate singular points of such equations (that is, for a (0, 0) =b (0, 0) =c (0, 0) =0): if two generic binary differential equations of this form are formally equivalent, then they are analytically equivalent. Bibliography: 36 titles.

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