Spectral isomorphisms of Morse flows
Downarowicz, T. ; Kwiatkowski, Jan ; Lacroix, Y.
Fundamenta Mathematicae, Tome 163 (2000), p. 193-213 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

A combinatorial description of spectral isomorphisms between Morse flows is provided. We introduce the notion of a regular spectral isomorphism and we study some invariants of such isomorphisms. In the case of Morse cocycles taking values in G=ℤp, where p is a prime, each spectral isomorphism is regular. The same holds true for arbitrary finite abelian groups under an additional combinatorial condition of asymmetry in the defining Morse sequence, and for Morse flows of rank one. Rank one is shown to be a spectral invariant in the class of Morse flows.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212439 
@article{bwmeta1.element.bwnjournal-article-fmv163i3p193bwm,
     author = {T. Downarowicz and Jan Kwiatkowski and Y. Lacroix},
     title = {Spectral isomorphisms of Morse flows},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {193-213},
     zbl = {1115.37303},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv163i3p193bwm}
}

Downarowicz, T.; Kwiatkowski, Jan; Lacroix, Y. Spectral isomorphisms of Morse flows. Fundamenta Mathematicae, Tome 163 (2000) pp. 193-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i3p193bwm/

[00000] [C-N] J. R. Choksi and M. G. Nadkarni, The maximal spectral type of a rank one transformation, Canad. Math. Bull. 37 (1994), 29-36. | Zbl 0793.28013

[00001] [D-L] T. Downarowicz and Y. Lacroix, Merit factors and Morse sequences, Theoret. Comput. Sci. 209 (1998), 377-387. | Zbl 0909.68125

[00002] [G] M. Guenais, Morse cocycles and simple Lebesgue spectrum, Ergodic Theory Dynam. Systems 19 (1999), 437-446. | Zbl 1031.37006

[00003] [J] A. del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (1977), 653-663. | Zbl 0335.28010

[00004] [J-L-M] A. del Junco, M. Lemańczyk and M. Mentzen, Semisimplicity, joinings and group extensions, Studia Math. 112 (1995), 141-164. | Zbl 0814.28007

[00005] [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, ibid. 110 (1994), 191-203. | Zbl 0810.28009

[00006] [K1] M. S. Keane, Generalized Morse sequences, Z. Wahrsch. Verw. Gebiete 10 (1968) 335-353.

[00007] [K2] M. S. Keane, Strongly mixing g-measures, Invent. Math. 16 (1972), 309-324. | Zbl 0241.28014

[00008] [Ki] J. King, The commutant is the weak closure of the powers, for rank-1 transformations, Ergodic Theory Dynam. Systems 6 (1986), 363-384. | Zbl 0595.47005

[00009] [Kw] J. Kwiatkowski, Spectral isomorphism of Morse dynamical systems, Bull. Acad. Polon. Sci. 29 (1981), 105-114. | Zbl 0496.28019

[00010] [K-S] J. Kwiatkowski and A. Sikorski, Spectral properties of G-symbolic Morse shifts, Bull. Soc. Math. France 115 (1987), 19-33. | Zbl 0624.28014

[00011] [L] M. Lemańczyk, The rank of regular Morse dynamical systems, Z. Wahrsch. Verw. Gebiete 70 (1985), 33-48. | Zbl 0549.28026

[00012] [M] J. C. Martin, The structure of generalized Morse minimal sets on n-symbols, Proc. Amer. Math. Soc. 2 (1977), 343-355. | Zbl 0375.28010

[00013] [N] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136. | Zbl 0425.28012