01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
7.11.1973
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 structure of the main limit sets (sets of periodic points, nonwandering points, $\omega$-limit sets) of monotone and piecewise monotone maps with a closed set of periodic points of dendrites with a closed set of brunch points of a finite order was studied (joint with L. S. Efremova). 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 Nizhni Novgorod State University in 1997 (department of differential equations and mathematical analysis). Ph.D. thesis was defended in 2001. A list of my works contains 15 titles.
Main publications:
L. S. Efremova, E. N. Makhrova, “The dynamics of a monotone mapping of an $n$-odd”, Russian Math. (Iz. VUZ), 41:10 (1997), 29–34
E. N. Makhrova, “Ob odnom primere kusochno-monotonnogo otobrazheniya dendrita”, Analiticheskie i chislennye metody v matematike i mekhanike, Trudy XXII konferentsii molodykh uchenykh mekhaniko-matematicheskogo fakulteta MGU (17–22 aprelya, 2000 g.), MGU, 2001, 112–114
L. S. Efremova, E. N. Makhrova, “The dynamics of monotone maps of dendrites”, Sb. Math., 192:6 (2001), 807–821
L. S. Efremova, E. N. Makhrova, “On homoclinic points of piecewice monotone mappings of dendrites”, Progress in Nonlinear Science, Int. Conf. dedicated to the 100-th anniversary of A. A. Andronov (Nizhny Novgorod, Russia July 2 - 6, 2001), 1, University of Nizhni Novgorod, 2002, 225–228
L. S. Efremova, E. N. Makhrova, “On the center of continuous maps of dendrites”, Journal of Difference Equations and Applications, 9:3/4 (2003), 381-392
L. S. Efremova, E. N. Makhrova, “O kusochno-monotonnykh otobrazheniyakh s zamknutym mnozhestvom periodicheskikh tochek”, Sovremennaya matematika i ee prilozheniya, 8, Trudy Mezhdunarodnoi konferentsii po dinamicheskim sistemam i differentsialnym uravneniyam, Suzdal, 1–6 iyulya 2002 g.:chast 2 (2003), 60–75
E. N. Makhrova, “O suschestvovanii periodicheskikh tochek nepreryvnykh otobrazhenii dendritov”, Nekotorye problemy fundamentalnoi i prikladnoi matematiki, 2007, Sbornik nauchnykh trudov MFTI, 133-141
E. N. Makhrova, “Homoclinic points and topological entropy of continuous mappings of a dendrite”, Journal of Math. Sciences, 158 (2009), 241–248
E. N. Makhrova, “The structure of dendrites with the periodic point property”, Russian Math. (Iz. VUZ), 55:11 (2011), 33–37
E. N. Makhrova, “The existence of a linear horseshoe of continuous maps of dendrites”, Russian Math. (Iz. VUZ), 57:3 (2013), 32–37
E. N. Makhrova, “Remarks on the Existence of Periodic Points for Continuous Maps on Dendrites”, Lobachevskii Journal of Mathematics, 43 (2022), 1711–1719
3.
L. S. Efremova, E. N. Makhrova, “One-dimensional dynamical systems”, Russian Math. Surveys, 76:5 (2021), 821–881
4.
E. N. Makhrova, “Monotone maps on dendrites”, Discontinuity, Nonlinearity, and Complexity, 9:4 (2020), 541-552
E. N. Makhrova, “Structure of dendrites and monotone maps on them”, Sbornik materialov Mezhdunarodnoi konferentsii KROMSh-2019 “XXX Krymskaya osennyaya matematicheskaya shkola-simpozium po spektralnym i evolyutsionnym zadacham”, "Poliprint, 2019, 140–142 (to appear)
7.
E. N. Makhrova, K. S. Vaniukova., “Dinamika gomeomorfizmov na kontinuumakh Peano”, Sbornik materialov Mezhdunarodnoi konferentsii KROMSh-2019 “XXX Krymskaya osennyaya matematicheskaya shkola-simpozium po spektralnym i evolyutsionnym zadacham”, “Poliprint”, 2019, 100
E. N. Makhrova, K. S. Vaniukova., “On the set of non-wandering points of monotone maps on local dendrites”, NOMA-15 International Workshop on Nonlinear Maps and Applications, Journal of Physics: Conference Series, 692., no. 1, 2016, 012012 , 10 pp. https://iopscience.iop.org/article/10.1088/1742-6596/692/1/012012
10.
E. N. Makhrova, “Structure of dendrites admitting an existence of arc horseshoe”, Russian Math. (Iz. VUZ), 59:8 (2015), 52–61
11.
E. N. Makhrova, “The existence of a linear horseshoe of continuous maps of dendrites”, Russian Math. (Iz. VUZ), 57:3 (2013), 32–37
12.
E. N. Makhrova, “The structure of dendrites with the periodic point property”, Russian Math. (Iz. VUZ), 55:11 (2011), 33–37
13.
E. N. Makhrova, “Homoclinic points and topological entropy of continuous mappings of a dendrite”, Journal of Math. Sciences, 158 (2009), 241–248
14.
E. N. Makhrova, “O suschestvovanii periodicheskikh tochek nepreryvnykh otobrazhenii dendritov”, Nekotorye problemy fundamentalnoi i prikladnoi matematiki, 2007, Sbornik nauchnykh trudov MFTI, 133-141
15.
L. S. Efremova, E. N. Makhrova, “On the center of continuous maps of dendrites”, Journal of Difference Equations and Applications, 9:3/4 (2003), 381-392
L. S. Efremova, E. N. Makhrova, “O kusochno-monotonnykh otobrazheniyakh s zamknutym mnozhestvom periodicheskikh tochek”, Sovremennaya matematika i ee prilozheniya, 8, Trudy Mezhdunarodnoi konferentsii po dinamicheskim sistemam i differentsialnym uravneniyam, Suzdal, 1–6 iyulya 2002 g.:chast 2 (2003), 60–75
17.
L. S. Efremova, E. N. Makhrova, “On homoclinic points of piecewice monotone mappings of dendrites”, Progress in Nonlinear Science, Int. Conf. dedicated to the 100-th anniversary of A. A. Andronov (Nizhny Novgorod, Russia July 2 - 6, 2001), 1, University of Nizhni Novgorod, 2002, 225–228
18.
E. N. Makhrova, “Ob odnom primere kusochno-monotonnogo otobrazheniya dendrita”, Analiticheskie i chislennye metody v matematike i mekhanike, Trudy XXII konferentsii molodykh uchenykh mekhaniko-matematicheskogo fakulteta MGU (17–22 aprelya, 2000 g.), MGU, 2001, 112–114
19.
L. S. Efremova, E. N. Makhrova, “The dynamics of monotone maps of dendrites”, Sb. Math., 192:6 (2001), 807–821
20.
L. S. Efremova, E. N. Makhrova, “The dynamics of a monotone mapping of an $n$-odd”, Russian Math. (Iz. VUZ), 41:10 (1997), 29–34
Presentations in Math-Net.Ru
1.
Topological entropy and minimal sets of continuous maps on ramified continua E. N. Makhrova III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 6, 2023 15:35
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