For bounded automatic actions of inverse semigroups the orbit relation is ω-regular, making first-order statements about orbits and actions decidable, including computability of Fatou component encodings for post-critically finite polynomials.
Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian
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Higher-dimensional substitution systems exhibit spectral pollution under periodic approximations, altering essential spectrum and Lebesgue measure in contrast to the one-dimensional case.
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Automatic actions I. Bounded automata and orbits
For bounded automatic actions of inverse semigroups the orbit relation is ω-regular, making first-order statements about orbits and actions decidable, including computability of Fatou component encodings for post-critically finite polynomials.
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Spectral pollution in substitution systems
Higher-dimensional substitution systems exhibit spectral pollution under periodic approximations, altering essential spectrum and Lebesgue measure in contrast to the one-dimensional case.