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
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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.
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