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Efremova, Lyudmila Sergeevna

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Total publications: 18
Scientific articles: 17
Presentations: 13

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Associate professor
Candidate of physico-mathematical sciences (1981)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 27.02.1952
E-mail: ,
Keywords: dynamical systems; differential and topological dynamics of discrete dynamical systems in low dimensions; one-dimensional dynamics; complex dynamics; chaotic dynamics.

Subject:

The problem of the coexistence of periods of periodic points of continuous maps of the circle was solved. Interdependence of arithmetic correlations between periods of periodic points with the degree of a continuous map of the circle is established. Criteria of the existence of homoclinic points of continuous endomorphisms of the circle and criteria of the disguishing of continuous endomorphisms of the circle with complicated dynamics (in the sense of A. N. Sharkovsky) are proved. The new concept of the investigation of skew products of interval maps based on the use of new set-valued functions (the $\Omega$-function and the $Bi$-function) of a skew product of interval maps was proposed. In the frames of this concept the dual nature of skew products of interval maps was explaned (it was established why some skew products of interval maps inherit the properties of interval maps, and others have the new properties which are not observed in interval maps). The criterion of the $\Omega$-stability of a skew product of interval maps in the space of $C^1$-smooth skew products of interval maps was proved. Nongenericity of $\Omega$-stability in the space of $C^1$-smooth skew products of interval maps was proved. The problem of the description of dynamics of the "most simple" continuous maps of dendrites with a closed set of brunch points of a finite order was formulated. A number of papers (joint with E. N. Makhrova) were devoted to the investigation of dynamics of monotone and piecewise monotone maps of dendrites with a closed set of periodic points. The possibility of the existence of piecewise monotone maps with fixed points and zero topological entropy possessing of the wandering homoclinic points; nonwandering, but not $\omega$-limit homoclinic points; $\omega$-limit homoclinic points on dendrites with a closed set of brunch points was determined.

Biography

Graduated from the Faculty of Mathematics and Mechanics of Gorky State University in 1974 (department of differential equations and mathematical analysis). PhD thesis was defended in 1981. A list of my works contains more than 40 titles. I deliver the lectures on contemporary problems of the theory of discrete dynamical systems for students, masters and post-graduates.

   
Main publications:
  • L. S. Efremova, New Set-valued Functions in the Theory of Skew Products of Interval Maps // Nonlinear Analysis. 47 (2001). P. 5297–5308.

http://www.mathnet.ru/eng/person8759
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/204958

Publications in Math-Net.Ru
2021
1. L. S. Efremova, E. N. Makhrova, “One-dimensional dynamical systems”, Uspekhi Mat. Nauk, 76:5(461) (2021),  81–146  mathnet
2017
2. L. S. Efremova, “Dynamics of skew products of interval maps”, Uspekhi Mat. Nauk, 72:1(433) (2017),  107–192  mathnet  mathscinet  elib; Russian Math. Surveys, 72:1 (2017), 101–178  isi  scopus
2016
3. L. S. Efremova, “Multivalued functions and nonwandering set of skew products of maps of an interval with complicated dynamics of quotient map”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, 2,  93–98  mathnet; Russian Math. (Iz. VUZ), 60:2 (2016), 77–81  isi  scopus
2015
4. L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, TMF, 185:2 (2015),  252–271  mathnet  mathscinet  elib; Theoret. and Math. Phys., 185:2 (2015), 1582–1598  isi  scopus
2013
5. L. S. Efremova, “Absence of $C^1$-$\Omega$-explosion in the space of smooth simplest skew products”, CMFD, 48 (2013),  36–50  mathnet; Journal of Mathematical Sciences, 202:6 (2014), 794–808  scopus
6. S. S. Bel'mesova, L. S. Efremova, “A one-parameter family of quadratic maps of a plane including Morse–Smale endomorphisms”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, 8,  80–85  mathnet; Russian Math. (Iz. VUZ), 57:8 (2013), 70–74  scopus
7. L. S. Efremova, “A decomposition theorem for the space of $C^1$-smooth skew products with complicated dynamics of the quotient map”, Mat. Sb., 204:11 (2013),  55–82  mathnet  mathscinet  zmath  elib; Sb. Math., 204:11 (2013), 1598–1623  isi  elib  scopus
2010
8. L. S. Efremova, “Differential properties and attracting sets of a simplest skew product of interval maps”, Mat. Sb., 201:6 (2010),  93–130  mathnet  mathscinet  zmath  elib; Sb. Math., 201:6 (2010), 873–907  isi  elib  scopus
9. L. S. Efremova, “Space of $C^1$-smooth skew products of maps of an interval”, TMF, 164:3 (2010),  447–454  mathnet; Theoret. and Math. Phys., 164:3 (2010), 1208–1214  isi  scopus
2006
10. L. S. Efremova, “On the nonwandering set and center of some skew products of mappings of the interval”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, 10,  19–28  mathnet  mathscinet  elib; Russian Math. (Iz. VUZ), 50:10 (2006), 17–25
2002
11. L. S. Efremova, “$\Omega$-Stable Skew Products of Interval Maps Are Not Dense in $T^1(I)$”, Trudy Mat. Inst. Steklova, 236 (2002),  167–173  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 236 (2002), 157–163
2001
12. L. S. Efremova, E. N. Makhrova, “The dynamics of monotone maps of dendrites”, Mat. Sb., 192:6 (2001),  15–30  mathnet  mathscinet  zmath; Sb. Math., 192:6 (2001), 807–821  isi  scopus
1999
13. L. S. Efremova, “On the concept of the $\Omega$-function of the skew product of interval mappings”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 67 (1999),  129–160  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 105:1 (2001), 1779–1798
1998
14. M. I. Voinova, L. S. Efremova, “Dynamics of elementary maps of dendrites”, Mat. Zametki, 63:2 (1998),  183–195  mathnet  mathscinet  zmath; Math. Notes, 63:2 (1998), 161–171  isi
1997
15. L. S. Efremova, E. N. Makhrova, “The dynamics of a monotone mapping of an $n$-odd”, Izv. Vyssh. Uchebn. Zaved. Mat., 1997, 10,  31–36  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 41:10 (1997), 29–34
1993
16. L. S. Efremova, “A class of twisted products of maps of an interval”, Mat. Zametki, 54:3 (1993),  18–33  mathnet  mathscinet  zmath; Math. Notes, 54:3 (1993), 890–898  isi
1985
17. L. S. Efremova, “A quotient of periods other than a power of two leads to chaos in a neighbourhood”, Uspekhi Mat. Nauk, 40:1(241) (1985),  197–198  mathnet  mathscinet  zmath; Russian Math. Surveys, 40:1 (1985), 217–218  isi

1994
18. L. S. Efremova, “Letter to the editor”, Mat. Zametki, 56:5 (1994),  141  mathnet; Math. Notes, 56:5 (1994), 1193–1194

Presentations in Math-Net.Ru
1. From Skew Products to Geometrically Integrable Maps in the Plane
L. S. Efremova
Conference «Hyperbolic Dynamics and Structural Stability» Dedicated to the 85th Anniversary of D. V. Anosov
November 12, 2021 13:00   
2. Простейший одномерный нехаотический аттрактор и гладкость косого произведения
L. S. Efremova
Function Theory, Operator Theory and Quantum Information Theory
October 7, 2021 12:00   
3. On the space of smooth geometrically integrable maps in the plane
L. S. Efremova
Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis – 2021
July 3, 2021 16:55   
4. Малые возмущения гладких косых произведений и свойство частичной интегрируемости
L. S. Efremova
Infinite dimensional analysis and mathematical physics
December 14, 2020 18:30
5. On the partial integrability property of maps obtained by small smooth perturbations of skew products
Lyudmila Efremova
International Conference on Mathematical Physics in Memory of Academic V. S. Vladimirov
November 24, 2020 18:30   
6. Гладкие возмущения косых произведений отображений интервала и свойство частичной интегрируемости
L. S. Efremova
Dynamical systems and differential equations
October 14, 2019 18:30
7. О гладких возмущениях косых произведений отображений интервала, приводящих к свойству частичной интегрируемости
L. S. Efremova
Dynamical systems and differential equations
March 18, 2019 18:30
8. Косые произведения в плоскости
L. S. Efremova
Dynamical systems and differential equations
February 26, 2018 18:30
9. Динамика косых произведений отображений интервала
L. S. Efremova
Infinite dimensional analysis and mathematical physics
February 12, 2018 18:30
10. Dynamics of skew products of interval maps
L. S. Efremova
Dobrushin Mathematics Laboratory Seminar
September 12, 2017 16:00
11. Main subspaces of the space of $C^1$-smooth skew products of interval maps
Lyudmila Efremova
International Conference “Anosov Systems and Modern Dynamics” dedicated to the 80th anniversary of Dmitry Anosov
December 22, 2016 17:00
12. On the complexity of skew products of maps of an interval
L. S. Efremova
The Seventh International Conference on Differential and Functional Differential Equations
August 25, 2014 18:25   
13. Integrability->Skew Products->Trace Maps
L. S. Efremova
International Conference on Differential Equations and Dynamical Systems
July 8, 2014 14:30

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