Abstract:This paper introduces the study of occurrence of symmetries in binary differential equations (BDEs). These are implicit differential equations given by the zeros of a quadratic 1-form, a(x, y)dy 2 +b(x, y)dxdy +c(x, y)dx 2 = 0, for a, b, c smooth real functions defined on an open set of R 2 . Generically, solutions of a BDE are given as leaves of a pair of foliations, and the action of a symmetry must depend not only whether it preserves or inverts the plane orientation, but also whether it preserves or interc… Show more
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