Periodic orbits of continuous mappings of the circle
Periodic orbits of continuous mappings of the circle
Let <italic>f</italic> be a continuous map of the circle into itself and let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P left-parenthesis f right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">P(f)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the set of positive integers <italic>n</italic> such that <italic>f</italic> has a periodic point …