Order and symmetry in birational difference equations and their signatures over finite phase spaces
نویسندگان
چکیده
We consider two classes of birational maps, or birational difference equations, that have structural properties defined by algebraic relations. The properties are possession of a rational integral and having a discrete time-reversal symmetry. We then consider how these algebraic structures constrain the distribution of orbit lengths of such maps when they are reduced over finite fields, giving a characteristic signature for each property. This can be exploited to test for such properties over the continuum.
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