Topological conjugations are not constructable
Linda Brown Westrick
TL;DR
This paper demonstrates that there exist pairs of computable topologically conjugate functions for which no conjugacy can be computed, answering an open question in the field of computable dynamics.
Contribution
It constructs explicit examples of conjugate functions with non-computable conjugacies, resolving a previously open problem.
Findings
Existence of non-computable conjugacies between computable functions
Explicit construction of such conjugate functions
Resolution of an open question by Kennedy and Stockman
Abstract
We construct two computable topologically conjugate functions for which no conjugacy is computable, or even hyperarithmetic, resolving an open question of Kennedy and Stockman.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Digital Image Processing Techniques