The critical exponent functions
Copyright policy )The critical exponent functions
The critical exponent of a finite or infinite word w over a given alphabet is the supremum of the reals α for which w contains an α-power. We study the maps associating to every real in the unit interval the inverse of the critical exponent of its base-n expansion. We strengthen a combinatorial result by J.D. Currie and N. Rampersad to show that these maps are left- or right-Darboux at every point, and use dynamical methods to show that they have infinitely many nontrivial fixed points and infinite topological entropy. Moreover, we show that our model-case map is topologically mixing.
- University of Camerino Italy
Baire class, Topological entropy, Combinatorial dynamics (types of periodic orbits), critical exponent, repetition, Combinatorics on words, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, words, alphabet, QA1-939, Notions of recurrence and recurrent behavior in topological dynamical systems, Word problems, etc. in computability and recursion theory, Mathematics
Baire class, Topological entropy, Combinatorial dynamics (types of periodic orbits), critical exponent, repetition, Combinatorics on words, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, words, alphabet, QA1-939, Notions of recurrence and recurrent behavior in topological dynamical systems, Word problems, etc. in computability and recursion theory, Mathematics
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