8 citations · 32 across the 13 of their papers we have counts for
13 papers
Double Hamiltonian Hopf Bifurcation: normalization and normal form non-integrability
L. M. Lerman, R. Mazrooei-Sebdani, N. E. Kulagin
The double Hamiltonian Hopf bifurcation is studied, i.e. a generic two-parametric unfolding of a smooth Hamiltonian system with four degrees of freedom which has at the critical va…
Symplectic Partially Hyperbolic Automorphisms of 6-Torus
L. M. Lerman, K. N. Trifonov
We study topological properties of automorphisms of a 6-dimensional torus generated by integer matrices symplectic with respect to either the standard symplectic structure in six-d…
Non-autonomous vector fields on : simple dynamics and wild separatrices embedding
V. Z. Grines, L. M. Lerman
We construct new substantive examples of non-autonomous vector fields on 3-dimensional sphere having a simple dynamics but non-trivial topology. The construction is based on two id…
Saddle-center and periodic orbit: dynamics near symmetric heteroclinic connection
L. M. Lerman, K. N. Trifonov
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a…
Solitons and cavitons in a nonlocal Whitham equation
N. Kulagin, L. Lerman, A. Malkin
Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth de…
Geometry of symplectic partially hyperbolic automorphisms on 4-torus
L. M. Lerman, K. N. Trifonov
We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a…
Abundance of entire solutions to nonlinear elliptic equations by the variational method
L. M. Lerman, P. E. Naryshkin, A. I. Nazarov
We study entire bounded solutions to the equation in . Our approach is purely variational and is based on concentration arguments and symmetry consi…
On interrelations between divergence-free and Hamiltonian dynamics
L. Lerman, E. Yakovlev
A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold and the dyna…
Nonautonomous gradient-like ODEs on the circle: classification, structural stability and autonomization
L. M. Lerman, E. V. Gubina
We study a class of scalar differential equations on the circle . This class is characterized mainly by the property that any solution of such an equation possesses exponentia…
Geometry of slow-fast Hamiltonian systems and Painlevé equations
L. M. Lerman, E. I. Yakovlev
In the first part of the paper we introduce some geometric tools needed to describe slow-fast Hamiltonian systems on smooth manifolds. We start with a smooth Poisson bundle $p: M\t…
Mixed Dynamics in a Parabolic Standard Map
L. M. Lerman, J. D. Meiss
We use numerical and analytical tools to demonstrate arguments in favor of the existence of a family of smooth, symplectic diffeomorphisms of the two-dimensional torus that have bo…
Separatrix splitting at a Hamiltonian bifurcation
Vassili Gelfreich, Lev Lerman
We discuss the splitting of a separatrix in a generic unfolding of a degenerate equilibrium in a Hamiltonian system with two degrees of freedom. We assume that the unperturbed fixe…
A saddle in a corner - a model of collinear triatomic chemical reactions
L. Lerman, V. Rom-Kedar
A geometrical model which captures the main ingredients governing atom-diatom collinear chemical reactions is proposed. This model is neither near-integrable nor hyperbolic, yet it…