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Spectral isomorphisms of Morse flows

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EN
Abstrakty
EN
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 $G = ℤ_p$, 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.
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Twórcy
  • Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland, downar@im.pwr.wroc.pl
  • Faculty of Mathematics and Informatics, Nicholas Copernicus, University Chopina 12/18, 87-100 Toruń, Poland, jkwiat@mat.uni.torun.pl
autor
  • Département de Mathématiques, Faculté des Sciences et Techniques, Université de Bretagne Occidentale, 6 Av. V. Le Gorgeu, B.P. 809 29285 Brest Cedex, France, lacroix@univ-brest.fr
Bibliografia
  • [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.
  • [D-L] T. Downarowicz and Y. Lacroix, Merit factors and Morse sequences, Theoret. Comput. Sci. 209 (1998), 377-387.
  • [G] M. Guenais, Morse cocycles and simple Lebesgue spectrum, Ergodic Theory Dynam. Systems 19 (1999), 437-446.
  • [J] A. del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (1977), 653-663.
  • [J-L-M] A. del Junco, M. Lemańczyk and M. Mentzen, Semisimplicity, joinings and group extensions, Studia Math. 112 (1995), 141-164.
  • [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, ibid. 110 (1994), 191-203.
  • [K1] M. S. Keane, Generalized Morse sequences, Z. Wahrsch. Verw. Gebiete 10 (1968) 335-353.
  • [K2] M. S. Keane, Strongly mixing g-measures, Invent. Math. 16 (1972), 309-324.
  • [Ki] J. King, The commutant is the weak closure of the powers, for rank-1 transformations, Ergodic Theory Dynam. Systems 6 (1986), 363-384.
  • [Kw] J. Kwiatkowski, Spectral isomorphism of Morse dynamical systems, Bull. Acad. Polon. Sci. 29 (1981), 105-114.
  • [K-S] J. Kwiatkowski and A. Sikorski, Spectral properties of G-symbolic Morse shifts, Bull. Soc. Math. France 115 (1987), 19-33.
  • [L] M. Lemańczyk, The rank of regular Morse dynamical systems, Z. Wahrsch. Verw. Gebiete 70 (1985), 33-48.
  • [M] J. C. Martin, The structure of generalized Morse minimal sets on n-symbols, Proc. Amer. Math. Soc. 2 (1977), 343-355.
  • [N] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv163i3p193bwm
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