Limit Theorem for the Hit Time of Mappings of a Circle with Break
Keywords:
homeomorphisms of a circle, hit time, rotation number
Abstract
In this paper, it is proved the limit theorem for distribution functions , of th entrance times in .
References
1. Arnold V.I. Small denominators I. On mappings of the circle onto yourself // Izv.AN SSSR.-1961.-№25(1).-S.21-86.
2. Kolmogorov A.N., Fomin S.V. Elements of the theory of functions and functional analysis. -M. : Nauka, 1976.
3. Kornfeld I.P., Sinai Ya.G., Fomin S.V. Ergodic theory. - M.: Nauka, 1980.
4. Feigenbaum M. J. Quantitative universality for a class of non-linear transformations//of Stat.Phys.-1978.-No.19(1).-R.25-52.
5. Herman M.R. Resultats recents sur la conjugaison differentiable. In Proc//Int. Math.Congress (Helsenki, 1978).-1980. -P. 811-820.
6. Katznelson Y., Ornstein D. The differentiability of the conjugation of certain diffeomorphisms of the circle// Ergodic Theory Dynam.Systems.-1989.- No. 9(4).-P.643-680.
7. Katznelson Y., Ornstein D. The absolute continuity of the conjugation of certain diffeomorphisms of the circle// Ergodic Theory Dynam.Systems.- 1989.- No. 9(4).-P.681-690.
8. Khanin K.M. Thermodynamic formalism for critical circle mappings// In Choas, ed. D.K.Campbell, American Institute of Physics, New York.-1990.- P.71-90.
9. Moser J. A rapid convergent iteration method and non-linear differential equations II // Ann.Scuola.Norm.Sup-Pisa.-1966.-№20(3)-P.499-535.
10. Ornstein D., Rudolph D., Wiess B. Equalence of measure preserving transformations// Memoirs of the AMS.-1982.-No. 26(37).
11. Poincare H. Memoire sur les courbes definie par une equation differentielle I IV// Math. Pures Appl., p. 1881-1886. Russian translation: On curves defined by differential equations. - M. L.: Gostekhizdat. - 1947.
12. Djalilov A.A., Khanin K.M. On the invariant measure for homeomorphisms of the circle with one break point// Zh. Functional analysis and its applications.-1998.-№32(3).-P.11-21.
13. Sinai Ya.G. Modern problems of ergodic theory. - M.: Publishing company "Physical and mathematical literature", 1995.
14. K. M. Khanin and E. B. Vul. Circle Homeomorphisms with weak Discontinuities. Advances in Soviet Mathematics, v. 3, 1991, p. 57-98.
15. Coelho Z., de Faria E. Limit laws of entrance times for homeomorphisms of the circle// Israel J.Math.-1996.- No. 93.-P.93-112.
16. Karshiboev H.K. Limit theorems for hit times for circle homeomorphisms with kinks // Materials international Conference “Differential Equations”. Almaty, September 24-26. - 2003.-p.97-98.
17. Dzhalilov A.A., Karshiboev Kh.K. Limit theorems for time circle mapping hits with one breakpoint //Advances in Mathematical Sciences. 2004, vol. 59. issue. 1(355). pp. 185-186.
18. Dzhalilov A.A., Karshiboev Kh.K. Thermodynamic formalism and circle homeomorphisms with a break-type singularity // Abdus Salam International Center for Theoretical Physics, Trieste, Italy. IC/2002/51.-p.30.
2. Kolmogorov A.N., Fomin S.V. Elements of the theory of functions and functional analysis. -M. : Nauka, 1976.
3. Kornfeld I.P., Sinai Ya.G., Fomin S.V. Ergodic theory. - M.: Nauka, 1980.
4. Feigenbaum M. J. Quantitative universality for a class of non-linear transformations//of Stat.Phys.-1978.-No.19(1).-R.25-52.
5. Herman M.R. Resultats recents sur la conjugaison differentiable. In Proc//Int. Math.Congress (Helsenki, 1978).-1980. -P. 811-820.
6. Katznelson Y., Ornstein D. The differentiability of the conjugation of certain diffeomorphisms of the circle// Ergodic Theory Dynam.Systems.-1989.- No. 9(4).-P.643-680.
7. Katznelson Y., Ornstein D. The absolute continuity of the conjugation of certain diffeomorphisms of the circle// Ergodic Theory Dynam.Systems.- 1989.- No. 9(4).-P.681-690.
8. Khanin K.M. Thermodynamic formalism for critical circle mappings// In Choas, ed. D.K.Campbell, American Institute of Physics, New York.-1990.- P.71-90.
9. Moser J. A rapid convergent iteration method and non-linear differential equations II // Ann.Scuola.Norm.Sup-Pisa.-1966.-№20(3)-P.499-535.
10. Ornstein D., Rudolph D., Wiess B. Equalence of measure preserving transformations// Memoirs of the AMS.-1982.-No. 26(37).
11. Poincare H. Memoire sur les courbes definie par une equation differentielle I IV// Math. Pures Appl., p. 1881-1886. Russian translation: On curves defined by differential equations. - M. L.: Gostekhizdat. - 1947.
12. Djalilov A.A., Khanin K.M. On the invariant measure for homeomorphisms of the circle with one break point// Zh. Functional analysis and its applications.-1998.-№32(3).-P.11-21.
13. Sinai Ya.G. Modern problems of ergodic theory. - M.: Publishing company "Physical and mathematical literature", 1995.
14. K. M. Khanin and E. B. Vul. Circle Homeomorphisms with weak Discontinuities. Advances in Soviet Mathematics, v. 3, 1991, p. 57-98.
15. Coelho Z., de Faria E. Limit laws of entrance times for homeomorphisms of the circle// Israel J.Math.-1996.- No. 93.-P.93-112.
16. Karshiboev H.K. Limit theorems for hit times for circle homeomorphisms with kinks // Materials international Conference “Differential Equations”. Almaty, September 24-26. - 2003.-p.97-98.
17. Dzhalilov A.A., Karshiboev Kh.K. Limit theorems for time circle mapping hits with one breakpoint //Advances in Mathematical Sciences. 2004, vol. 59. issue. 1(355). pp. 185-186.
18. Dzhalilov A.A., Karshiboev Kh.K. Thermodynamic formalism and circle homeomorphisms with a break-type singularity // Abdus Salam International Center for Theoretical Physics, Trieste, Italy. IC/2002/51.-p.30.
Published
2023-04-06
How to Cite
[1]
Kilichovich, K.K. 2023. Limit Theorem for the Hit Time of Mappings of a Circle with Break. International Journal on Integrated Education. 6, 4 (Apr. 2023), 71-77. DOI:https://doi.org/10.17605/ijie.v6i4.4235.
Section
Articles
In submitting the manuscript to the International Journal on Integrated Education (IJIE), the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere,
- The publication has been approved by the author(s) and by responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
License and Copyright Agreement
Authors who publish with International Journal on Integrated Education (IJIE) agree to the following terms:
- Authors retain copyright and grant the International Journal on Integrated Education (IJIE) right of first publication with the work simultaneously licensed under Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors can enter into separate, additional contractual arrangements for the non-exclusive distribution of the International Journal on Integrated Education (IJIE) published version of the work (e.g., post it to an institutional repository or edit it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
1.png)
