Babbage equation on the circle
Copyright policy )Babbage equation on the circle
Charles Babbage dealt with equations of the form \(\varphi^n(x)=x\) where \(\varphi^n\) denotes the \(n\)-th iterate already back in 1815. Here, \(\varphi\) is an unknown function of a set into itself and \(n\) is a positive integer. Hence the problem is to find functions of a certain class on a specified set for which the \(n\)-th iterate is the identity. The present paper describes all continuous self-mappings of the unit circle.
iterative root, Iteration theory, iterative and composite equations, unit circle, Iteration of real functions in one variable, continuous self-mappings, Babbage equation
iterative root, Iteration theory, iterative and composite equations, unit circle, Iteration of real functions in one variable, continuous self-mappings, Babbage equation
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