Dr. Nikita Begun
Department of Mathematics and Computer Science, Institute of Mathematics
Group Hysteresis Dynamics
Group Mathematics of Machine Learning
Postdoc
Room 141
14195 Berlin
Research interests
- Dynamical systems
- Differential equations
- Reaction-diffusion equations
- Hyperbolic attractors
- Systems with dry friction
- Machine learning
Projects
- Reaction-diffusion systems: hysteresis and nonlocal interactions
(Project A9 of the DFG Collaborative Research Center 910 on Control of self-organizing nonlinear systems) - Machine learning: Hysteretic neural networks
Begun N., Kravetc P., Rachinskii D.
Chaos in Saw Map
Submitted, arXiv 1709.01962 (2018)
(pdf)
Begun N., Pliss V. A., Sell G.
On the stability of weakly hyperbolic invariant sets
Journal of Differential Equations, Vol. 262, No. 4, pp. 3194-3213. 2017.
(pdf)
Arnold M., Begun N., Gurevich P., Kwame E., Lamba H., Rachinskii D.
Dynamics of discrete time systems with a hysteresis stop operator.
SIAM Journal on Applied Dynamical Systems. Vol. 16, No. 1, pp. 91-119. 2017
(pdf)
Begun N., Pliss V. A., Sell G.
On the stability of hyperbolic attractors of systems of differential equations
Differential Equations. Vol. 52, No. 2, pp. 139-148. 2016
(pdf)
Begun N.
Perturbations of weakly hyperbolic invariant sets of two-dimensional periodic systems.
Vestnik St. Petersburg University: Mathematics, Vol. 48, No 1, pp. 1-8 (2015)
(pdf)
Begun N., Kryzhevich S.
One-dimensional chaos in a system with dry friction: analytical approach
Meccanica, Vol. 50, No. 8, pp. 1935-1948 (2015)
(pdf)
Begun N.
On the stability of invariant sets of leaves of three-dimensional periodic systems.
Vestnik St. Petersburg University. Mathematics, Vol. 47, No. 3, pp. 95-101. 2014.
(pdf)
Begun N.
On the closure of the leaf invariant set of perturbed system.
Differential Equations and Control Processes. No 1. 80-88. 2013.
(pdf)
Begun N.
On the stability of sheet invariant sets of swo-dimensional periodic systems.
Vestnik St. Petersburg University. Mathematics, Vol. 45, No. 4, pp. 145-152. 2012.
(pdf)
Begun N., Pilyugin S. Yu.
Analogues of Takens theorems for generalized actions of the group Z∞.
Vestnik St. Petersburg University. Mathematics, Vol. 43, No. 4, pp. 198-203. 2010.
(pdf)
Begun N.
On the existence of square-integrable solutions for systems with weak nonlinearity.
Vestnik St. Petersburg University. Mathematics, Vol. 43, No. 2, pp. 74-81. 2010.
(pdf)