Local symmetries in the period-doubling sequence

Discrete Applied Mathematics

Volumn 100, Issue 1-2, 2000, Pages 115-121

  Damanik, David ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

68R15; Combinatorics on words; Local symmetries; Period doubling sequence

Indexed keywords

EID: 0011968521     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00199-7     Document Type: Article

References (24)

1. Allouche J.-P. Schrödinger operators with Rudin-Shapiro potentials are not palindromic. J. Math. Phys. 38:1997;1843-1848.
2. M. Baake, A note on palindromicity, preprint.
3. Bellissard J., Bovier A., Ghez J.-M. Spectral properties of a tight-binding Hamiltonian with period doubling potential. Comm. Math. Phys. 135:1991;379-399.
4. Bellissard J., Bovier A., Ghez J.-M. Gap labelling theorems for one-dimensional discrete Schrödinger operators. Rev. Math. Phys. 4:1992;1-37.
5. Bellissard J., Iochum B., Scoppola E., Testard D. Spectral properties of one-dimensional quasi-crystals. Comm. Math. Phys. 125:1989;527-543.
6. Bovier A., Ghez J.-M. Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions. Comm. Math. Phys. 158:1993;45-66.
7. Bovier A., Ghez J.-M. Erratum: spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions. Comm. Math. Phys. 166:1994;431-432.
8. Damanik D. α -continuity properties of one-dimensional quasicrystals Comm. Math. Phys. 192:1998;169-182.
9. Damanik D. Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure. Commun. Math. Phys. 196:1998;477-483.
10. Damanik D. Singular continuous spectrum for a class of substitution Hamiltonians. Lett. Math. Phys. 46:1998;303-311.
11. D. Damanik, On the measure of the set of strongly palindromic sequences in strictly ergodic subshifts over finite alphabets, in preparation.
12. Delyon F., Petritis D. Absence of localization in a class of Schrödinger operators with quasiperiodic potential. Commun. Math. Phys. 103:1986;441-444.
13. Delyon F., Peyrière J. Recurrence of the eigenstates of a Schrödinger operator with automatic potential. J. Stat. Phys. 64:1991;363-368.
14. Droubay X. Palindromes in the Fibonacci word. Inform. Process. Lett. 55:1995;217-221.
15. X. Droubay, G. Pirillo, Palindromes and Sturmian words, Theor. Comp. Sci., to appear.
16. Hof A., Knill O., Simon B. Singular continuous spectrum for palindromic Schrödinger operators. Commun. Math. Phys. 174:1995;149-159.
17. Iochum B., Testard D. Power law growth for the resistance in the Fibonacci model. J. Statist. Phys. 65:1991;715-723.
18. Iochum B., Raymond L., Testard D. Resistance of one-dimensional quasicrystals. Physica. A187:1992;353-368.
19. Marcus S., Mateescu A., Paun G., Salomaa A. On symmetry in strings, sequences and languages. Internat. J. Comput. Math. 54:1994;1-13.
20. M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Mathematics, Vol. 1284, Springer, Berlin, 1987.
21. L. Raymond, A constructive gap labelling for the discrete Schrödinger operator on a quasiperiodic chain, preprint.
22. N.J.A. Sloane, A Handbook of Integer Sequences, Academic Press, New York, 1973.
23. Süto A. The spectrum of a quasiperiodic Schrödinger operator. Comm. Math. Phys. 111:1987;409-415.
24. Süto A. Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian. J. Statist. Phys. 56:1989;525-531.