Ergodic Theory Lecture Notes I apologise that no corrections with respect to the original have been yet incorporated, will do soon.
Studying dynamical systems over topological Markov chains: Markov partitions Lecture notes (12 Nov 2009)
Studying dynamical systems over topological Markov chains: Markov partitions Lecture notes (12+18 Nov 2009 update)
Proof of the existence of an interval where periodic points of a monotone discountinuous map are dense Lecture notes (26 Jan 2010)
Current research interests:
Dynamics of nonsmooth systems in a neighborhood of grazing
Regularization of nonsmooth systems
Smoothness of nonautonomous differential equations with Lipschitz right hand terms
Applications of topological degree
Implicit function theorem
Preprints:
• A. Buica, J. Llibre, O. Makarenkov, Bifurcations from nondegenerate families of periodic solutions,
ArXiv Preprint.
• O. Makarenkov, Asymptotic stability of oscillations of two-bodies vibrating screen with one-sided obstacle without clearances,
ArXiv Preprint.
• O. Makarenkov, F. Verhulst, Bifurcation of asymptotically stable periodic solutions in nearly impact oscillators,
ArXiv Preprint.
• O. Makarenkov, Lipschitz perturbations of differentiable implicit functions,
ArXiv Preprint.
Publications:
[1] M. Kamenskii, O. Makarenkov, P. Nistri, An alternative approach to study bifurcation from a limit cycle
in periodically perturbed autonomous systems, Journal of Dynamics and Differential Equations, accepted,
ArXiv Preprint.
[2] O. Makarenkov, R. Ortega, Asymptotic stability of forced oscillations emanating from a limit cycle, J. Differential Equations 250 (2011), no 1, 39-52.
ArXiv Preprint.
[3] O. Makarenkov, L. Malaguti, P. Nistri, On the behavior of periodic solutions of
planar autonomous Hamiltonian systems
with multivalued periodic perturbations, Z. Anal. Anwendungen 30 (2011), no 2., 129-144. Preprint.
[4] O. Makarenkov, Stability of non-sticking oscillations in systems with piecewise smooth discontinuous perturbations,
in "Problems of Analytical Mechanics and Stability Theory, Collection of papers dedicated to the memory of Academician Valentin V. Rumyantsev."
- M.: Fizmatlit (2009), 272-284.
Article (rus)
[5] O. Makarenkov, Poincare index and periodic solutions of perturbed autonomous systems, Trans.
Mosc. Math. Soc. 70 (2009) 4-45. Preprint, Article (rus),
Article (eng)
[6] A. Buica, J. Llibre, O. Makarenkov, Asymptotic stability of periodic solutions for nonsmooth
differential equations with application to nonsmooth van der Pol oscillator, SIAM J. Math. Anal. 40 (2009), no. 6, 2478-2495.
Preprint, Article
[7] O. Makarenkov, Influence of a small perturbation on Poincare-Andronov operators with not well
defined topological degree, Topol. Methods Nonlinear Anal. 32 (2008), no. 1, 165-176.
Preprint, Article
[8] M. Kamenskii, O. Makarenkov, P. Nistri, Periodic bifurcation from families of periodic solutions
for semilinear differential equations with Lipschitzian perturbations in Banach spaces,
Adv. Nonlinear Stud. 8 (2008), no. 2, 271-288.
Preprint, Article
[9] A. Buica, J. Llibre, O. Makarenkov, To Mitropol'skii Yu.A.'s theorem on periodic solutions of
systems of nonlinear differential equations with non-differentiable right-hand-side, Dokl. Math.
Sci. 421 (2008), no. 3, 302-304.
Preprint (eng),
Preprint (rus),
Article (eng)
Article (rus)
[10] O. Makarenkov, P. Nistri, On the rate of convergence of periodic solutions in perturbed autonomous
systems as the perturbation vanishes, Commun. Pure Appl. Anal. 7 (2008), no. 1,
49-61.
Preprint, Article
[11] M. Kamenskii, O. Makarenkov, P. Nistri, A continuation principle for a class of periodically
perturbed autonomous systems, Math. Nachr. 281 (2008), no. 1, 42-61.
Preprint, Article
[12] O. Makarenkov, P. Nistri, D. Papini, Synchronization problems for unidirectional feedback
coupled nonlinear systems, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 15 (2008),
no. 4, 453-468.
Preprint, Article
[13] O. Makarenkov, P. Nistri, Periodic solutions for planar autonomous systems with nonsmooth
periodic perturbations, J. Math. Anal. Appl. 338 (2008), no. 2, 1401-1417.
Preprint, Article
[14] M. Kamenskii, O. Makarenkov, P. Nistri, Periodic solutions of periodically perturbed planar
autonomous systems: A topological approach, Adv. Differential Equations 11 (2006), no. 4, 399-418.
Preprint, Article
[15] M. Kamenskii, O. Makarenkov, P. Nistri, Small parameter perturbations of nonlinear periodic
systems, Nonlinearity 17 (2004), no. 1, 193-205.
Preprint, Article
[16] M. Kamenskii, O. Makarenkov, P. Nistri, Periodic solutions for a class of singulary perturbated
systems, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 11 (2004), no. 1, 41-55.
Preprint, Article
[17] M. Kamenskii, O. Makarenkov, P. Nistri, A new approach in the theory of ordinary differential
equations with small parameter, Dokl. Math. Sci. 67 (2003), 36-38 (english) Dokl. Akad. Nauk 388 (2003), no. 4, 439-442 (Russian).
Preprint (eng),
Preprint (rus),
Article