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Mosc. Math. J., 2006, Volume 6, Number 2, Pages 317–351 (Mi mmj249)  

This article is cited in 12 scientific papers (total in 12 papers)

The rigidity problem for analytic critical circle maps

D. V. Khmelev, M. Yampolskya

a Department of Mathematics, University of Toronto

Abstract: It is shown that if $f$ and $g$ are any two analytic critical circle mappings with the same irrational rotation number, then the conjugacy that maps the critical point of $f$ to that of $g$ has regularity $C^{1+\alpha}$ at the critical point, with a universal value of $\alpha>0$. As a consequence, a new proof of the hyperbolicity of the full renormalization horseshoe of critical circle maps is given.

Key words and phrases: Critical circle mapping, rigidity, renormalization.

DOI: https://doi.org/10.17323/1609-4514-2006-6-2-317-351

Full text: http://www.ams.org/.../abst6-2-2006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37E10
Received: November 12, 2005
Language:

Citation: D. V. Khmelev, M. Yampolsky, “The rigidity problem for analytic critical circle maps”, Mosc. Math. J., 6:2 (2006), 317–351

Citation in format AMSBIB
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\by D.~V.~Khmelev, M.~Yampolsky
\paper The rigidity problem for analytic critical circle maps
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 2
\pages 317--351
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\crossref{https://doi.org/10.17323/1609-4514-2006-6-2-317-351}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2270617}
\zmath{https://zbmath.org/?q=an:1124.37024}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595800005}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Khanin K., Teplinsky A., “Robust rigidity for circle diffeomorphisms with singularities”, Invent. Math., 169:1 (2007), 193–218  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Diaz-Espinosa O., de la Liave R., “Renormalization and central limit theorem for critical dynamical systems with weak external noise”, J. Mod. Dyn., 1:3 (2007), 477–543  crossref  mathscinet  zmath  isi
    3. de Melo W., “Rigidity in dynamics”, Bull. Belg. Math. Soc. Simon Stevin, 15:5 (2008), 789–796  mathscinet  zmath  isi  elib
    4. De Melo W., “Renormalization in one-dimensional dynamics”, J. Difference Equ. Appl., 17:8 (2011), 1185–1197  crossref  mathscinet  zmath  isi  scopus
    5. Avila A., “On Rigidity of Critical Circle Maps”, Bull. Braz. Math. Soc., 44:4 (2013), 611–619  crossref  mathscinet  zmath  isi  elib  scopus
    6. De Faria E., Guarino P., “Real Bounds and Lyapunov Exponents”, Discret. Contin. Dyn. Syst., 36:4 (2016), 1957–1982  crossref  mathscinet  zmath  isi
    7. Kocic S., “Generic Rigidity For Circle Diffeomorphisms With Breaks”, Commun. Math. Phys., 344:2 (2016), 427–445  crossref  mathscinet  zmath  isi  scopus
    8. Guarino P., de Melo W., “Rigidity of Smooth Critical Circle Maps”, J. Eur. Math. Soc., 19:6 (2017), 1729–1783  crossref  zmath  isi  scopus
    9. Khanin K., Kocic S., “Robust Local Holder Rigidity of Circle Maps With Breaks”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 35:7 (2018), 1827–1845  crossref  mathscinet  zmath  isi  scopus
    10. Guarino P., Martens M., de Melo W., “Rigidity of Critical Circle Maps”, Duke Math. J., 167:11 (2018), 2125–2188  crossref  mathscinet  zmath  isi  scopus
    11. Estevez G., De Faria E., “Real Bounds and Quasisymmetric Rigidity of Multicritical Circle Maps”, Trans. Am. Math. Soc., 370:8 (2018), 5583–5616  crossref  mathscinet  zmath  isi  scopus
    12. Estevez G., de Faria E., Guarino P., “Beau Bounds For Multicritical Circle Maps”, Indag. Math.-New Ser., 29:3 (2018), 842–859  crossref  mathscinet  zmath  isi  scopus
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