Spectral isomorphisms of Morse flows

T. Downarowicz; Jan Kwiatkowski; Y. Lacroix

Fundamenta Mathematicae (2000)

  • Volume: 163, Issue: 3, page 193-213
  • ISSN: 0016-2736

Abstract

top
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.

How to cite

top

Downarowicz, T., Kwiatkowski, Jan, and Lacroix, Y.. "Spectral isomorphisms of Morse flows." Fundamenta Mathematicae 163.3 (2000): 193-213. <http://eudml.org/doc/212439>.

@article{Downarowicz2000,
abstract = {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.},
author = {Downarowicz, T., Kwiatkowski, Jan, Lacroix, Y.},
journal = {Fundamenta Mathematicae},
keywords = {Morse sequence; spectral isomorphism},
language = {eng},
number = {3},
pages = {193-213},
title = {Spectral isomorphisms of Morse flows},
url = {http://eudml.org/doc/212439},
volume = {163},
year = {2000},
}

TY - JOUR
AU - Downarowicz, T.
AU - Kwiatkowski, Jan
AU - Lacroix, Y.
TI - Spectral isomorphisms of Morse flows
JO - Fundamenta Mathematicae
PY - 2000
VL - 163
IS - 3
SP - 193
EP - 213
AB - 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.
LA - eng
KW - Morse sequence; spectral isomorphism
UR - http://eudml.org/doc/212439
ER -

References

top
  1. [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. Zbl0793.28013
  2. [D-L] T. Downarowicz and Y. Lacroix, Merit factors and Morse sequences, Theoret. Comput. Sci. 209 (1998), 377-387. Zbl0909.68125
  3. [G] M. Guenais, Morse cocycles and simple Lebesgue spectrum, Ergodic Theory Dynam. Systems 19 (1999), 437-446. Zbl1031.37006
  4. [J] A. del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (1977), 653-663. Zbl0335.28010
  5. [J-L-M] A. del Junco, M. Lemańczyk and M. Mentzen, Semisimplicity, joinings and group extensions, Studia Math. 112 (1995), 141-164. Zbl0814.28007
  6. [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, ibid. 110 (1994), 191-203. Zbl0810.28009
  7. [K1] M. S. Keane, Generalized Morse sequences, Z. Wahrsch. Verw. Gebiete 10 (1968) 335-353. 
  8. [K2] M. S. Keane, Strongly mixing g-measures, Invent. Math. 16 (1972), 309-324. Zbl0241.28014
  9. [Ki] J. King, The commutant is the weak closure of the powers, for rank-1 transformations, Ergodic Theory Dynam. Systems 6 (1986), 363-384. Zbl0595.47005
  10. [Kw] J. Kwiatkowski, Spectral isomorphism of Morse dynamical systems, Bull. Acad. Polon. Sci. 29 (1981), 105-114. Zbl0496.28019
  11. [K-S] J. Kwiatkowski and A. Sikorski, Spectral properties of G-symbolic Morse shifts, Bull. Soc. Math. France 115 (1987), 19-33. Zbl0624.28014
  12. [L] M. Lemańczyk, The rank of regular Morse dynamical systems, Z. Wahrsch. Verw. Gebiete 70 (1985), 33-48. Zbl0549.28026
  13. [M] J. C. Martin, The structure of generalized Morse minimal sets on n-symbols, Proc. Amer. Math. Soc. 2 (1977), 343-355. Zbl0375.28010
  14. [N] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136. Zbl0425.28012

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.