Behavior of a class of nonlinear discrete-time systems

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A novel collection of nonlinear discrete-time systems is analyzed and characterized up to isomorphism. The systems in question are autonomous and deterministic and have the half-open unit interval [0, 1) as state space. The analysis establishes isomorphisms between these systems and the members of an especially simple, easy-to-understand, normal-form subclass of “prototype” systems. The prototypes consist exclusively of piecewise-linear systems with parallel pieces. The theory hinges upon a generally unfamiliar but remarkable real number representation resembling ordinary binary or decimal notation but involving a radix or base which is not an integer.

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论文评审过程:Received 10 August 1983, Accepted 15 March 1985, Available online 2 December 2003.

论文官网地址:https://doi.org/10.1016/0022-0000(85)90064-9