Lev Lerman
25/12 Bolshaya Pecherskaya Str., Nizhny Novgorod
Research University Higher School of Economics
Publications:
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Lerman L. M.
What I Did in Dynamics
2025, Vol. 21, no. 1, pp. 15-31
Abstract
This text presents a loose journey on my activity over the scientific life on the background of
the rapid development of the theory of dynamical systems during the last 50 years. I intentionally
do not explain nor go into mathematical details, otherwise this would require too many pages.
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Lerman L. M., Turaev D. V.
On symmetry breaking bifurcations in reversible systems
2012, Vol. 8, No. 2, pp. 323-343
Abstract
We review results on local bifurcations in reversible systems (flows and diffeomorphisms) which lead to the creation of pairs attractor-repellor at bifurcations from symmetric equilibria (for flows) and fixed points (for diffeomorphisms). We consider bifurcations of co-dimension 1 in systems of small dimensions (2,3, and 4).
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Afraimovich V. S., Belyakov L. A., Bykov V. V., Gonchenko S. V., Lerman L. M., Lukyanov V. I., Malkin M. I., Morozov A. D., Turaev D. V.
Leonid Pavlovich Shilnikov (17.12.1934–26.12.2011)
2012, Vol. 8, No. 1, pp. 183-186
Abstract
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Lerman L. M., Slinyakova N. A.
On the dynamics of the piecewise-linear model of the Swift–Hohenberg equation
2009, Vol. 5, No. 4, pp. 569-583
Abstract
In this paper we study the piecewise-linear model of the stationary Swift—Hohenberg equation well known in mathematical physics, which provides explicit front type solutions. Due to the reversibility relative to two involutions of the corresponding Hamiltonian system, this involves the existence of a heteroclinic contour connecting two saddle-foci. Using methods of symbolic dynamics, we give a description of all solutions lying in the neighborhood of the contour at the level of the Hamiltonian containing the contour.
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