Vol. 52, No. 1, 1974

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Global reflection for a class of simple closed curves

James McLean Sloss

Vol. 52 (1974), No. 1, 247–260

Global reflection is considered for a class of closed Jordan curves Γ : [x(𝜃),y(𝜃)],0 𝜃 < 27τ where x(𝜃) and y(𝜃) are trigonometric polynomials. Every curve of this form is algebraic and global reflection across it reduces to investigating an algebraic function and its critical points. The reflection function is picked to be that solution of the algebraic equation that maps Γ : [x(𝜃),y(𝜃)] pointwise into [x(𝜃),y(𝜃)]. This function is defined and analytic except on a finite set of points inside Γ, and at each of these points it is continuous.

Mathematical Subject Classification
Primary: 30A14
Received: 17 January 1973
Published: 1 May 1974
James McLean Sloss