Inverse polynomial images which consists of two Jordan arcs—An algebraic solution

Inverse polynomial images which consists of two Jordan arcs - An algebraic solution

Inverse polynomial images of [−1, 1], which consists of two Jordan arcs, are characterised by an explicit polynomial equation for the four endpoints of the arcs. MSC: 41A10; 30C10

Description of Inverse Polynomial Images which Consist of Two Jordan Arcs with the Help of Jacobi’s Elliptic Functions∗

First we discuss the description of inverse polynomial images of [−1, 1], which consists of two Jordan arcs, by the endpoints of the arcs only. The polynomial which generates the two Jordan arcs is given explicitly in terms of Jacobi’s theta functions. Then the main emphasis is put on the case where the two arcs are symmetric with respect to the real line. For instance it is demonstrated that t...

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