On the growth rate inequality for self-maps of the sphere

Let Sm = {x02 + x12 + < middle dot >< middle dot >+ x2m = 1} and P = {x0 = x1 = 0} boolean AND Sm. Suppose f is a self-map of Sm such that f-1(P) = P and | deg(f|P )|< | deg(f)|. Then, the number of fixed points of f n grows at least exponentially with base |d|> 1, where d = deg(f)/ deg(f|P) is an element of Z.

​Let Sm = {x02 + x12 + < middle dot >< middle dot >+ x2m = 1} and P = {x0 = x1 = 0} boolean AND Sm. Suppose f is a self-map of Sm such that f-1(P) = P and | deg(f|P )|< | deg(f)|. Then, the number of fixed points of f n grows at least exponentially with base |d|> 1, where d = deg(f)/ deg(f|P) is an element of Z. Read More

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