On a "structure intermediate between quasiperiodic and random"

Journal of Statistical Physics

Volumn 84, Issue 1-2, 1996, Pages 309-320

  Hof, A ^a,b  

^a MCMASTER UNIVERSITY   (Canada)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Aperiodic structures; Diffraction; Flow under a function; Periodic approximation; Singular continuous spectrum; Weak mixing

Indexed keywords

EID: 0030186880     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02179589     Document Type: Article

References (23)

1. S. Aubry, C. Godrèche, and J. M. Luck, A structure intermediate between quasiperiodic and random, Europhys. Lett. 4:639-643 (1987).
2. S. Aubry, C. Godrèche, and J. M. Luck, Scaling properties of a structure intermediate between quasiperiodic and random, J. Stat. Phys. 51:1033-1074 (1988).
3. H. Kesten, On a conjecture of Erdös and Szüsz related to uniform distribution mod 1, Acta Arithm. 12:193-212 (1966).
4. A. Guinier, X-Ray Diffraction (Dover, New York, 1994).
5. A. Hof, On diffraction by aperiodic structures, Commun. Math. Phys. 169:25-43 (1995).
6. B. Simon, Operators with singular continuous spectrum: I. General operators, Ann. Math. 1995:131-145.
7. J. von Neumann, Zur Operatorenmethode in der Klassischen Mechanik, Ann. Math. 33:587-642 (1932).
8. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic Theory (Springer-Verlag, Berlin, 1982).
9. R. B. Israel, Convexity in the Theory of Lattice Gases (Princeton University Press, Princeton, New Jersey, 1979).
10. S. Dworkin, Spectral theory and X-ray diffraction, J. Math. Phys. 34:2965-2967 (1993).
11. K. Merrill, Cohomology of step functions under irrational rotations, Isr. J. Math. 52:320-340 (1985).
12. L. Baggett, On circle-valued cocycles of an ergodic measure preserving transformation, Isr. J. Math. 61:29-38 (1988).
13. H. Furstenberg, Strict ergodicity and transformation of the torus, Am. J. Math. 88:573-601 (1961).
14. A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Russ. Math. Surv. 22:77-102 (1968).
15. W. A. Veech, Strict ergodicity in zero dimensional dynamical systems and the Kronecker Weyl theorem mod 2, Trans. Am. Math. 140:1-33 (1969).
16. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed. (Oxford University Press, Oxford, 1956).
17. M. Steward, Irregularities of uniform distributions, Acta Math. Acad. Scient. Hung. 37:185-221 (1981).
18. W. A. Veech, Topological dynamics, Bull. Am. Math. Soc. 83:775-830 (1977).
19. O. Knill, Singular continuous spectrum in ergodic theory, Preprint California Institute of Technology (1995) [Available as paper 95-193 on mp arc@math.utexas.edu].
20. M. Reed and B. Simon, Methods of Modern Mathematical Physics I. Functional Analysis, rev. enlarged ed. (Academic Press, 1980).
21. A. V. Kočergin, Time changes in Hows and mixing, Math. USSR Izv. 7:1273-1294 (1973).
22. A. V. Kočergin, On the absence of mixing in special flows over the rotation of a circle and in flows on a two-dimensional torus, Sov. Math. Dokl. 13:949-952 (1972).
23. W. Parry, Topics in Ergodic Theory (Cambridge University Press, Cambridge, 1981).