-
Previous Article
Well-posedness and asymptotic behavior of solutions for the Blackstock-Crighton-Westervelt equation
- DCDS Home
- This Issue
-
Next Article
Topological and ergodic properties of symmetric sub-shifts
Renormalizations of circle hoemomorphisms with a single break point
1. | Faculty of Mathematics and Mechanics. Samarkand State University, Boulevard Street 15, 140104 Samarkand, Uzbekistan |
2. | Turin Politechnic University in Tashkent, Kichik halqa yuli 17, 100095 Tashkent, Uzbekistan |
3. | Institut für Theoretische Physik, TU Clausthal, Leibnizstrasse 10, D-38678 Clausthal-Zellerfeld, Germany |
References:
[1] |
V. I. Arnol'd, Small denominators: I. Mappings from the circle onto itself, Izv. Akad. Nauk SSSR, Ser. Mat., 25 (1961), 21-86. |
[2] |
H. Akhadkulov, A. Dzhalilov and D. Mayer, On conjugations of circle homeomorphisms with two break points, Ergod. Theor. and Dynam. Syst., 34 (2014), 725-741.
doi: 10.1017/etds.2012.159. |
[3] |
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer-Verlag, New York, 1982.
doi: 10.1007/978-1-4615-6927-5. |
[4] |
A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl., 11 (1932), 333-375. |
[5] |
A. A. Dzhalilov and K. M. Khanin, On invariant measure for homeomorphisms of a circle with a point of break, Funct. Anal. Appl., 32 (1998), 153-161.
doi: 10.1007/BF02463336. |
[6] |
A. A. Dzhalilov and I. Liousse, Circle homeomorphismswith two break points, Nonlinearity, 19 (2006), 1951-1968.
doi: 10.1088/0951-7715/19/8/010. |
[7] |
A. A. Dzhalilov, I. Liousse and D. Mayer, Singular measures of piecewise smooth circle homeomorphisms with two break points, Discrete and continuous dynamical systems, 24 (2009), 381-403.
doi: 10.3934/dcds.2009.24.381. |
[8] |
A. A. Dzhalilov, H. Akin and S. Temir, Conjugations between circle maps with a single break point, Journal of Mathematical Analysis and Applications, 366 (2010), 1-10.
doi: 10.1016/j.jmaa.2009.12.050. |
[9] |
A. A. Dzhalilov, D. Mayer and U. A. Safarov, Piecwise-smooth circle homeomorphisms with several break points, Izvestiya RAN: Ser. Mat., 76 (2012), 101-120, translation of Izvestiya: Mathematics, 76 (2012), 94-112. |
[10] |
E. de Faria and W. de Melo, Rigidity of critical circle mappings, I. J. Eur. Math. Soc. (JEMS), 1 (1999), 339-392.
doi: 10.1007/s100970050011. |
[11] |
M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Etudes Sci. Publ. Math., 49 (1979), 5-233.
doi: 10.1007/BF02684798. |
[12] |
Y. Katznelson and D. Ornstein, The differentability continuity of the conjugation of certain diffeomorphisms of the circle, Ergod. Theor. Dyn. Syst., 9 (1989), 643-680.
doi: 10.1017/S0143385700005277. |
[13] |
Y. Katznelson and D. Ornstein, The absolute continuity of the conjugation of certain diffeomorphisms of the circle, Ergod. Theor. Dyn. Syst., 9 (1989), 681-690 .
doi: 10.1017/S0143385700005289. |
[14] |
K. M. Khanin and Ya. G. Sinai, Smoothness of conjugacies of diffeomorphisms of the circle with rotations, Russ. Math. Surv., 44 (1989), 69-99, translation of Usp. Mat. Nauk, 44 (1989), 57-82.
doi: 10.1070/RM1989v044n01ABEH002008. |
[15] |
K. M. Khanin and E. B. Vul, Circle homeomorphisms with weak discontinuities, Advances in Soviet Mathematics, 3 (1991), 57-98. |
[16] |
K. M. Khanin and D. Khmelev, Renormalizations and Rigidity Theory for Circle Homeomorphisms with Singularities of the Break Type, Commun. Math. Phys., 235 (2003), 69-124.
doi: 10.1007/s00220-003-0809-5. |
[17] |
I. Liousse, PL Homeomorphisms of the circle which are piecewise $C^1$ conjugate to irrational rotations, Bull. Braz. Math. Soc., 35 (2004), 269-280.
doi: 10.1007/s00574-004-0014-y. |
[18] |
J. Stark, Smooth conjugacy and renormalization for diffeomorfisms of the circle, Nonlinearity, 1 (1988), 541-575.
doi: 10.1088/0951-7715/1/4/004. |
[19] |
G. Swiatek, Rational rotation number for maps of the circle, Commun. Math. Phys., textbf{119} (1988), 109-128.
doi: 10.1007/BF01218263. |
[20] |
M. Stein, Groups of piecewise linear homeomorphisms, Trans. A.M.S., 332 (1992), 477-514.
doi: 10.1090/S0002-9947-1992-1094555-4. |
[21] |
A. Yu. Teplinskii and K. M. Khanin, Robust rigidity for circle diffeomorphisms with singularities, Inventiones mathematicae, 169 (2007), 193-218.
doi: 10.1007/s00222-007-0047-0. |
[22] |
J. C. Yoccoz, Il n'y a pas de contre-exemple de Denjoy analytique, C. R. Acad. Sci. Paris, 298 (1984), 141-144. |
show all references
References:
[1] |
V. I. Arnol'd, Small denominators: I. Mappings from the circle onto itself, Izv. Akad. Nauk SSSR, Ser. Mat., 25 (1961), 21-86. |
[2] |
H. Akhadkulov, A. Dzhalilov and D. Mayer, On conjugations of circle homeomorphisms with two break points, Ergod. Theor. and Dynam. Syst., 34 (2014), 725-741.
doi: 10.1017/etds.2012.159. |
[3] |
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer-Verlag, New York, 1982.
doi: 10.1007/978-1-4615-6927-5. |
[4] |
A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl., 11 (1932), 333-375. |
[5] |
A. A. Dzhalilov and K. M. Khanin, On invariant measure for homeomorphisms of a circle with a point of break, Funct. Anal. Appl., 32 (1998), 153-161.
doi: 10.1007/BF02463336. |
[6] |
A. A. Dzhalilov and I. Liousse, Circle homeomorphismswith two break points, Nonlinearity, 19 (2006), 1951-1968.
doi: 10.1088/0951-7715/19/8/010. |
[7] |
A. A. Dzhalilov, I. Liousse and D. Mayer, Singular measures of piecewise smooth circle homeomorphisms with two break points, Discrete and continuous dynamical systems, 24 (2009), 381-403.
doi: 10.3934/dcds.2009.24.381. |
[8] |
A. A. Dzhalilov, H. Akin and S. Temir, Conjugations between circle maps with a single break point, Journal of Mathematical Analysis and Applications, 366 (2010), 1-10.
doi: 10.1016/j.jmaa.2009.12.050. |
[9] |
A. A. Dzhalilov, D. Mayer and U. A. Safarov, Piecwise-smooth circle homeomorphisms with several break points, Izvestiya RAN: Ser. Mat., 76 (2012), 101-120, translation of Izvestiya: Mathematics, 76 (2012), 94-112. |
[10] |
E. de Faria and W. de Melo, Rigidity of critical circle mappings, I. J. Eur. Math. Soc. (JEMS), 1 (1999), 339-392.
doi: 10.1007/s100970050011. |
[11] |
M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Etudes Sci. Publ. Math., 49 (1979), 5-233.
doi: 10.1007/BF02684798. |
[12] |
Y. Katznelson and D. Ornstein, The differentability continuity of the conjugation of certain diffeomorphisms of the circle, Ergod. Theor. Dyn. Syst., 9 (1989), 643-680.
doi: 10.1017/S0143385700005277. |
[13] |
Y. Katznelson and D. Ornstein, The absolute continuity of the conjugation of certain diffeomorphisms of the circle, Ergod. Theor. Dyn. Syst., 9 (1989), 681-690 .
doi: 10.1017/S0143385700005289. |
[14] |
K. M. Khanin and Ya. G. Sinai, Smoothness of conjugacies of diffeomorphisms of the circle with rotations, Russ. Math. Surv., 44 (1989), 69-99, translation of Usp. Mat. Nauk, 44 (1989), 57-82.
doi: 10.1070/RM1989v044n01ABEH002008. |
[15] |
K. M. Khanin and E. B. Vul, Circle homeomorphisms with weak discontinuities, Advances in Soviet Mathematics, 3 (1991), 57-98. |
[16] |
K. M. Khanin and D. Khmelev, Renormalizations and Rigidity Theory for Circle Homeomorphisms with Singularities of the Break Type, Commun. Math. Phys., 235 (2003), 69-124.
doi: 10.1007/s00220-003-0809-5. |
[17] |
I. Liousse, PL Homeomorphisms of the circle which are piecewise $C^1$ conjugate to irrational rotations, Bull. Braz. Math. Soc., 35 (2004), 269-280.
doi: 10.1007/s00574-004-0014-y. |
[18] |
J. Stark, Smooth conjugacy and renormalization for diffeomorfisms of the circle, Nonlinearity, 1 (1988), 541-575.
doi: 10.1088/0951-7715/1/4/004. |
[19] |
G. Swiatek, Rational rotation number for maps of the circle, Commun. Math. Phys., textbf{119} (1988), 109-128.
doi: 10.1007/BF01218263. |
[20] |
M. Stein, Groups of piecewise linear homeomorphisms, Trans. A.M.S., 332 (1992), 477-514.
doi: 10.1090/S0002-9947-1992-1094555-4. |
[21] |
A. Yu. Teplinskii and K. M. Khanin, Robust rigidity for circle diffeomorphisms with singularities, Inventiones mathematicae, 169 (2007), 193-218.
doi: 10.1007/s00222-007-0047-0. |
[22] |
J. C. Yoccoz, Il n'y a pas de contre-exemple de Denjoy analytique, C. R. Acad. Sci. Paris, 298 (1984), 141-144. |
[1] |
Malo Jézéquel. Parameter regularity of dynamical determinants of expanding maps of the circle and an application to linear response. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 927-958. doi: 10.3934/dcds.2019039 |
[2] |
Akhtam Dzhalilov, Isabelle Liousse, Dieter Mayer. Singular measures of piecewise smooth circle homeomorphisms with two break points. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 381-403. doi: 10.3934/dcds.2009.24.381 |
[3] |
Qiudong Wang. The diffusion time of the connecting orbit around rotation number zero for the monotone twist maps. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 255-274. doi: 10.3934/dcds.2000.6.255 |
[4] |
Michel Laurent, Arnaldo Nogueira. Rotation number of contracted rotations. Journal of Modern Dynamics, 2018, 12: 175-191. doi: 10.3934/jmd.2018007 |
[5] |
Christopher Cleveland. Rotation sets for unimodal maps of the interval. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 617-632. doi: 10.3934/dcds.2003.9.617 |
[6] |
Abdelhamid Adouani, Habib Marzougui. Computation of rotation numbers for a class of PL-circle homeomorphisms. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3399-3419. doi: 10.3934/dcds.2012.32.3399 |
[7] |
Rafael De La Llave, Michael Shub, Carles Simó. Entropy estimates for a family of expanding maps of the circle. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 597-608. doi: 10.3934/dcdsb.2008.10.597 |
[8] |
Alena Erchenko. Flexibility of Lyapunov exponents for expanding circle maps. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2325-2342. doi: 10.3934/dcds.2019098 |
[9] |
Liviana Palmisano. Unbounded regime for circle maps with a flat interval. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2099-2122. doi: 10.3934/dcds.2015.35.2099 |
[10] |
Héctor E. Lomelí. Heteroclinic orbits and rotation sets for twist maps. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 343-354. doi: 10.3934/dcds.2006.14.343 |
[11] |
Wenxian Shen. Global attractor and rotation number of a class of nonlinear noisy oscillators. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 597-611. doi: 10.3934/dcds.2007.18.597 |
[12] |
Zhihong Xia, Peizheng Yu. A fixed point theorem for twist maps. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 4051-4059. doi: 10.3934/dcds.2022045 |
[13] |
Liviana Palmisano, Bertuel Tangue Ndawa. A phase transition for circle maps with a flat spot and different critical exponents. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5037-5055. doi: 10.3934/dcds.2021067 |
[14] |
Jan J. Dijkstra and Jan van Mill. Homeomorphism groups of manifolds and Erdos space. Electronic Research Announcements, 2004, 10: 29-38. |
[15] |
Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017 |
[16] |
Luis Hernández-Corbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 2979-2995. doi: 10.3934/dcds.2015.35.2979 |
[17] |
Joachim Escher, Boris Kolev. Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle. Journal of Geometric Mechanics, 2014, 6 (3) : 335-372. doi: 10.3934/jgm.2014.6.335 |
[18] |
Stefano Galatolo, Alfonso Sorrentino. Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 815-839. doi: 10.3934/dcds.2021138 |
[19] |
M . Bartušek, John R. Graef. Some limit-point/limit-circle results for third order differential equations. Conference Publications, 2001, 2001 (Special) : 31-38. doi: 10.3934/proc.2001.2001.31 |
[20] |
Fawwaz Batayneh, Cecilia González-Tokman. On the number of invariant measures for random expanding maps in higher dimensions. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5887-5914. doi: 10.3934/dcds.2021100 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]