B. R. Fayad, A. B. Katok, A. Windsor, “Mixed spectrum reparameterizations of linear flows on $\mathbb T^2$”, Mosc. Math. J., 1:4 (2001), 521

Moscow Mathematical Journal

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Moscow Mathematical Journal, 2001, Volume 1, Number 4, Pages 521–537
DOI: https://doi.org/10.17323/1609-4514-2001-1-4-521-537 (Mi mmj34)

This article is cited in 21 scientific papers (total in 21 papers)

Mixed spectrum reparameterizations of linear flows on

$\mathbb T^2$

B. R. Fayad^ab, A. B. Katok^a, A. Windsor^a

^a Department of Mathematics, Pennsylvania State University
^b Université Paris 13

Full-text PDF Citations (21)

References:

PDF

HTML

DOI: https://doi.org/10.17323/1609-4514-2001-1-4-521-537

Abstract: We prove the existence of mixed spectrum

$C^\infty$ reparameterizations of any linear flow on

$\mathbb T^2$ with Liouville rotation number. For a restricted class of Liouville rotation numbers, we prove the existence of mixed spectrum real-analytic reparameterizations.

Key words and phrases: Mixed spectrum, reparameterization, special flow, Liouville, cocycle.

Received: September 26, 2001; in revised form December 23, 2001

Bibliographic databases:

MSC: 37A20, 37A45, 37C05

Language: English

Citation: B. R. Fayad, A. B. Katok, A. Windsor, “Mixed spectrum reparameterizations of linear flows on

$\mathbb T^2$ ”, Mosc. Math. J., 1:4 (2001), 521–537

Citation in format AMSBIB

\Bibitem{FayKatWin01}

\by B.~R.~Fayad, A.~B.~Katok, A.~Windsor

\paper Mixed spectrum reparameterizations of linear flows on~$\mathbb T^2$

\jour Mosc. Math.~J.

\yr 2001

\vol 1

\issue 4

\pages 521--537

\mathnet{http://mi.mathnet.ru/mmj34}

\crossref{https://doi.org/10.17323/1609-4514-2001-1-4-521-537}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1901073}

\zmath{https://zbmath.org/?q=an:1123.37300}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000208587600003}

\elib{https://elibrary.ru/item.asp?id=8379085}

Linking options:

https://www.mathnet.ru/eng/mmj34

https://www.mathnet.ru/eng/mmj/v1/i4/p521

This publication is cited in the following 21 articles:

Xiaolong He, “Simultaneous conjugation of commuting foliation preserving torus maps”, Proc. Amer. Math. Soc., 2023
Adam Kanigowski, Mariusz Lemańczyk, Encyclopedia of Complexity and Systems Science Series, Ergodic Theory, 2023, 109
Xiaolong He, Rafael de la Llave, “Resonances and Phase Locking Phenomena for Foliation Preserving Torus Maps”, SIAM J. Appl. Dyn. Syst., 22:1 (2023), 382
Pablo Guarino, Pierre-Antoine Guihéneuf, Bruno Santiago, “Dirac Physical Measures on Saddle-Type Fixed Points”, J Dyn Diff Equat, 34:2 (2022), 983
BORIS HASSELBLATT, “Anatole Katok”, Ergod. Th. Dynam. Sys., 42:2 (2022), 321
Fayad B., Forni G., Kanigowski A., “Lebesgue Spectrum of Countable Multiplicity For Conservative Flows on the Torus”, J. Am. Math. Soc., 34:3 (2021), 747–813
Adam Kanigowski, Mariusz Lemańczyk, Encyclopedia of Complexity and Systems Science, 2020, 1
Huang W., Xu L., “Special Flow, Weak Mixing and Complexity”, Commun. Math. Stat., 7:1 (2019), 85–122
Boubel Ch., Mounoud P., “Affine Transformations and Parallel Lightlike Vector Fields on Compact Lorentzian 3-Manifolds”, Trans. Am. Math. Soc., 368:3 (2016), 2223–2262
You J., Zhou Q., “Embedding of Analytic Quasi-Periodic Cocycles Into Analytic Quasi-Periodic Linear Systems and its Applications”, Commun. Math. Phys., 323:3 (2013), 975–1005
Huguet G., de la Llave R., Sire Ya., “Computation of Whiskered Invariant Tori and their Associated Manifolds: New Fast Algorithms”, Discrete and Continuous Dynamical Systems, 32:4 (2012), 1309–1353
Tiedra De Aldecoa R., “Spectral Analysis of Time Changes of Horocycle Flows”, J. Mod. Dyn., 6:2 (2012), 275–285
Gemma Huguet, Rafael de la Llave, Yannick Sire, “Computation of whiskered invariant tori and their associated manifolds: New fast algorithms”, Discrete & Continuous Dynamical Systems - A, 32:4 (2012), 1309
Mariusz Lemańczyk, Mathematics of Complexity and Dynamical Systems, 2012, 1618
Mariusz Lemańczyk, Encyclopedia of Complexity and Systems Science, 2009, 8554
A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252
Fayad B., Windsor A., “A dichotomy between discrete and continuous spectrum for a class of special flows over rotations”, Journal of Modern Dynamics, 1:1 (2007), 107–122
Fayad B., “Smooth mixing flows with purely singular spectra”, Duke Mathematical Journal, 132:2 (2006), 371–391
Anatole Katok, Jean-Paul Thouvenot, Handbook of Dynamical Systems, 1, 2006, 649
Fraczek K., Lemanczyk M., “A class of special flows over irrational rotations which is disjoint from mixing flows”, Ergodic Theory and Dynamical Systems, 24:4 (2004), 1083–1095

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	278
References:	85

Registration to the website

Logotypes