Speciality:
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.
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
