## Dzhalilov Akhtam Abdurakhmanovich

### Professor

**Date and place of birth:**

**Nationality:** Uzbek

**Education:** High

**Academic degree:** Doctor of Physical and Mathematical Sciences

**Academic rank:** Professor

**E-mail: ** a.dzhalilov@polito.uz

**Phone: **+998 71 2462087

#### Academic degrees

• Bachelor & Master, 1979, Moscow State University, Russia

• Ph.D., in Mathematics and Physics, 1987, Moscow State University, Russia

Thesis title: “Thermodynamic Formalism for the Systems of Statistical Mechanics and Small Perturbations of One Dimensional Maps”. Thesis Advisor Prof. Yakov Sinai

• Doctor of Sciences in Physics and Mathematics, 2000, Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent

Thesis title: “Analysis of One Dimensional Maps with Singularities by Methods of Statistical Mechanics”

#### Employment/career

• General working experience – 36 years

• Professional experience – 30 years

#### Awards and Honors

• 2011, 2012: Fulbright Visiting Scholar, Stony Brook University, USA

• 2007, 2008, 2009, 2010, 2011, 2013: Research Fellowship, German

• Research Foundation (DFG), Germany

• 2002, 2004, 2005: Research Fellowship, The Royal Society, England

• 1998, 2001, 2002, 2010: Research Fellowship, Abdus Salam ICTP, Italy

• 2004: Research Fellowship, DAAD, Germany

• 2004: Research Fellowship of Lill 1 University, France

• 2007, 2008: Research Fellowship, TUBITAK, Turkey

• Senior Associate of the International Centre for Theoretical Physics (ICTP), 2015-2021.

#### Research Interests

Dynamical Systems, Ergodic Theory, Probability Theory, Analysis, Statistical Mechanics

#### Supervision of PhD Thesis

• Akhadkulov Habibulla, National University of Uzbekistan, 2008

• Karshiboev Khayrulla , National University of Uzbekistan, 2012

• Begmatov Abdumajid, National University of Uzbekistan, 2012

• Safarov Utkir, National University of Uzbekistan, 2012

• Poshohodjaeva Gulnora, Samarkand State University, on the process

#### Main Publications

1. A. Begmatov, A.A. Dzhalilov, D. Mayer: Renormalizations of circle maps with a single break point, Discrete and Continuous Dynamical Systems, Series A, Volume 34, Issue 11, pp. 4487 – 4513, (2014)

2. H. Akhadkulov, A.A.Dzhalilov , M. S. Noorani: On conjugacies between piecewise-smooth circle maps, Nonlinear Analysis, 99, p.1-15, (2014)

3. H. Akhadkulov, A. Dzhalilov, D. Mayer : “On conjugations of circle homeomor-phisms with two break points, Ergodic Theory and Dynamical Systems, v.34, N 03, pp. 725-741, (2013)

4. A. Dzhalilov, Mohd Salmi Md Noorani, H. Akhadkulov: Stronger version of Denjoy type inequality, Bulletin of the Malaysian Mathematical Sciences Society,(2013)

5. A. Dzhalilov, Mohd Salmi MdNoorani, H. Akhadkulov: On Invariant Measure of the Circle Maps. Journal of Physics, Conference Series, Volume 435, Issue 1, article id. 012011,( 2013).

6. A. Dzhalilov, S. Akhadkulov and M. S. Noorani: On critical circle homeomorphisms with infinite number of break points, Hindawi Publishing Corporation Abstract and Applied Analysis. Article ID 378742, pp.1-6, (2013)

7. A.A. Dzhalilov, D. Mayer and U.A.Safarov: Conjugacies between P-homeomorphisms with several breaks. http://arxiv.org/abs/1408.5732.

8. A. Dzhalilov, D. Mayer, U. Safarov: Piecewise-smooth circle homeomorphisms with several break points, Izvestiya RAN: Ser. Mat. v.76, N1, p.95-113, (2012). English transl.: Izvestiya RAN: Ser. Mat. v.76, N1, p.101-120,( 2012)

9. A.Dzhalilov, H. Akin, S.Temir: Conjugations between circle maps with a single break point, Journal of Mathematical Analysis and Applications 366, p.1-10, (2011) .

10. A. Dzhalilov, A. Begmatov: Renormalizations of circle homeomorphisms with a break point, TWMS Jour. Pure Appl. Math., V.2, N.1, pp.54-65, (2011).

11. A. Dzhalilov, A.Yu.Teplinskii: Counterexamples to rigidity theory of circle diffeomorphisms with breaks, Doklady Akademii Nauk Ukrainy, N9, p.18-23, (2010) .

12. I. Liousse, A.A.Dzhalilov, D. Mayer: “Singular measures of piecewise smooth circle homeomorphisms with two break points”, Discrete and Continuous Dynamical Systems Series A (DCDS-A) v. 24, N 2, p. 381 -403, (2009 )

13. A. Dzhalilov, Farmanov and U. Safarov: Invariant Distributions of circle homeomorphisms with several break points, DokladyAkad. NaukUsbekistana, N3, p. 3-8 ( 2009) (in Russian)

14. A. Dzhalilov, A. Begmatov: Renormalizations of circle homeomorphisms satisfying the Kaznelson-Ornstein conditions, Uzbek Math.Jour., N2, p. 49-58,( 2008) (in Russian)

15. A.A. Dzhalilov, I. Liousse: Circle homeomorphisms with two break points, Nonlinearity, v.19, N 8, p.1951-1968, (2006).

16. A. Dzhalilov: Renormalizations of Circle Diffeomorphisms, Doklady Akad. Nauk Usbekistana, N1, p.17-20, (2006).

17. A. Dzhalilov and Kh. K.Karshibaev: Limit Theorems of Entrance Times for Circle Homeomorphisms with one Point of Break, Uspehi Matem. Nauk, v.59, N1,p. 200-202, 218.2004 (in Russian). English transl.: Russian Mathematical Surveys, v.59, N1,( 2004).

18. A. Dzhalilov: Limit Laws of Entrance Times for Critical Circle Maps, Theoretical and Mathematical Physics, v.138, N2, p.181-199, 2004 (in Russian). English transl.: Theoretical and Mathematical Physics, v.138, N2, p.190-207, (2004).

19. A. Dzhalilov: Thermodynamic Formalism and Singular Measures for Critical Circle Maps, Theoretical and Mathematical Physics, v.134, N2, p.190-206, 2003 (in Russian). English transl.: Theoretical and Mathematical Physics, v.134, N2, p.166-180, (2003)

20. A. Dzhalilov and Kh. K. Karshibaev: Distributions of Entrance Times for Circle Homeomorphisms with Break-type Singularity, Uzbek Math. Jorn., N2, p. 9-16, 2003 (in Russian)

21. A. Dzhalilov and Kh. K.Karshibaev: Thermodynamic Formalism and Circle Homeomorphisms with Break-type Singularity, Preprint, 30p, IC/2002/51, Abdus Salam ICTP, Trieste (Italy),( 2002).

22. A. Dzhalilov: On Behaviour of Metric Haracteristics of a Circle Homeomorphisms with Break Singularities, Uzbek Math. Jorn., N1, p.11-14, 2000 (in Russian)

23. A. Dzhalilov: Singular Invariant Measures of Circle Homeomorphisms with Point of Break, UspehiMatem. Nauk, v.54, N4, p.165-166, 1999 (in Russian) English transl.: Russian Mathematical Surveys, v.54, N4,( 1999).

24. A. Dzhalilov: Piecewise Smoothness of Conjugate Homeomorphisms of a Circle with Corners, Theoretical and Mathematical Physics, v.120, N 2, p.961-972, 1999 (in Russian). English transl.: Theoretical and Mathematical Physics, v.120, N 2, p.179-192, 1999

25. A. Dzhalilov: The Holder Property of Singular Invariant Measure of Circle Homeomorphisms with Single Corners, Theoretical and Mathematical Physics, v.121, N 3, p.355-366, 1999 (in Russian). English transl.: Theoretical and Mathematical Physics, v.121, N3, p.1557-1566, (1999).

26. A. Dzhalilov: Metrical Properties of One Family of Homeomorphisms of a Circle with Corners, Uzbek Math. Jorn., N2, p.19- 36,1999 (in Russian)

27. A. Dzhalilov and K. M. Khanin: On an Invariant Measure for Homeomorphisms of a Circle with a Point of Break, Functional Analysis and its Applications, v.32, N 3 , p.11-21, 1998 (in Russian). English transl.: Functional Analysis andits Applications, v.32, N3, p.153-161, (1998)

28. A. Dzhalilov: Thermodynamic Formalism for the Family of Circle Homeomorphisms with Break Singularities, Uzbek Math. Jorn. N1, p. 35-44, (1998) (in Russian)

29. A. Dzhalilov: Spectral and Metrical Properties for Circle Homeomorphisms with a Point of Break, Dokl.Akad.Nauk. Respubl.Uzbekistan, N2, p. 9-12, (1998) (in Russian)

30. A. Dzhalilov: Singularity Exponents of Invariant Measures of the Circle Homeomorphisms with Break Singularity, Uzbek Math. Jorn., N4, p.29-38, (1998) (in Russian)

31. A. Dzhalilov and K.M.Khanin: On an Invariant Measure for Homeomorphisms of the Circle with a Single Break Point, UspehiMatem. Nauk, v.51, N 6, p.201-202, 1996 (in Russian). English transl.: Russian Math. Surveys v.51, N.6, p. 1198-1199, (1996)

32. A. Dzhalilov: Thermodynamic Formalism for Critical Circle Homeomorphisms, Uzbek Math. Jorn. N3, p. 21-30, (1995) (in Russian)

33. A. Dzhalilov and K.M. Khanin: Spectral Properties of Infnite Sequences of Doubling Period Bifurcations and Thermodynamic Formalism I, Uzbek Math. Jorn. N 1, p. 23-34,( 1992) (in Russian)

34. A. Dzhalilov and K.M. Khanin: Spectral Properties of Infinite Sequences of Doubling Period Bifurcations and Thermodynamic Formalism II, Uzbek Math. Jorn. N5, p. 27- 39, (1992) (in Russian)

35. A. Dzhalilov: The Toda Chain in the Thermodynamical Limit, UspehiMathem. Nauk, v.40, N1, p.191-192, 1985 (in Russian), English transl.: Russian Mathematical Surveys, v.40, N1, p.213- 214, (1985).

36. A. Dzhalilov and V.A. Chulaevskii: Thermodynamic Properties of the Peierls Model, Theoretical and Mathematical Phisics, v.63, N3, p.458-464, 1985 (in Russian). English transl.: Theoretical and Mathematical Physics, v.63, N3, p.630-636, (1985).