45 citations · 274 across the 22 of their papers we have counts for
22 papers
Behaviour of trajectories near a two-cycle heteroclinic network
Olga Podvigina
We study behaviour of trajectories near a type Z heteroclinic network which is a union of two cycles. Analytical and numerical studies indicate that attractiveness of this network…
Impact of a moon on the evolution of a planet's obliquity: a non-resonant case
O. M. Podvigina, P. S. Krasilnikov
We investigate how the variation of the obliquity (the axial tilt) of a hypothetical exo-Earth is effected by the presence of a satellite, an exo-Moon. Namely, we study analyticall…
Asymptotic stability of robust heteroclinic networks
Olga Podvigina, Sofia B. S. D. Castro, Isabel S. Labouriau
We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable. We study the asymptotic stability of ac-networks --- robust heter…
Simple heteroclinic networks in
Olga Podvigina, Alexander Lohse
We classify simple heteroclinic networks for a -equivariant system in with finite , proceeding as follows: we define a graph associated with…
Stability of a heteroclinic network and its cycles: a case study from Boussinesq convection
Olga Podvigina, Sofia B. S. D. Castro, Isabel S. Labouriau
This article is concerned with three heteroclinic cycles forming a heteroclinic network in . The stability of the cycles and of the network are studied. The cycles a…
Pseudo-simple heteroclinic cycles in
Pascal Chossat, Alexander Lohse, Olga Podvigina
We study pseudo-simple heteroclinic cycles for a -equivariant system in with finite , and their nearby dynamics. In particular, in a first step towards a fu…
Asymptotic stability of pseudo-simple heteroclinic cycles in R^4
Olga Podvigina, Pascal Chossat
Robust heteroclinic cycles in equivariant dynamical systems in R^4 have been a subject of intense scientific investigation because, unlike heteroclinic cycles in R^3, they can have…
The Cauchy-Lagrangian method for numerical analysis of Euler flow
O. Podvigina, V. Zheligovsky, U. Frisch
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of…
Simple heteroclinic cycles in R^4
Olga Podvigina, Pascal Chossat
In generic dynamical systems heteroclinic cycles are invariant sets of codimension at least one, but they can be structurally stable in systems which are equivariant under the acti…
Existence, uniqueness and analyticity of space-periodic solutions to the regularised long-wave equation
R. Chertovskih, A. C. -L. Chian, O. Podvigina +2
We consider space-periodic evolutionary and travelling-wave solutions to the regularised long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and…
Classification and stability of simple homoclinic cycles in R^5
Olga Podvigina
The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple…
Optimal transport by omni-potential flow and cosmological reconstruction
Uriel Frisch, Olga Podvigina, Barbara Villone +1
One of the simplest models used in studying the dynamics of large-scale structure in cosmology, known as the Zeldovich approximation, is equivalent to the three-dimensional invisci…
Stability and bifurcations of heteroclinic cycles of type Z
Olga Podvigina
Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper we study stability properti…
The onset of convection in a rotating layer of viscous fluid with an imposed magnetic field: dependence on the Prandtl numbers
Olga Podvigina
We consider the onset of Boussinesq convection in a horizontal layer of electrically conducting incompressible fluid with rigid electrically insulating horizontal boundaries. The f…
On local attraction properties and a stability index for heteroclinic connections
Olga Podvigina, Peter Ashwin
Some invariant sets may attract a nearby set of initial conditions but nonetheless repel a complementary nearby set of initial conditions. For a given invariant set …
On stability of rolls near the onset of convection in a layer with stress-free boundaries
Olga Podvigina
We consider a classical problem of linear stability of convective rolls in a plane layer with stress-free horizontal boundaries near the onset of convection. The problem has been s…
The Monge-Ampere equation: various forms and numerical methods
V. Zheligovsky, O. Podvigina, U. Frisch
We present three novel forms of the Monge-Ampere equation, which is used, e.g., in image processing and in reconstruction of mass transportation in the primordial Universe. The cen…
Dependence of magnetic field generation by thermal convection on the rotation rate: a case study
R. Chertovskih, S. M. A. Gama, O. Podvigina +1
Dependence of magnetic field generation on the rotation rate is explored by direct numerical simulation of magnetohydrodynamic convective attractors in a plane layer of conducting…
Generation of multiscale magnetic field by parity-invariant time-periodic flows
V. A. Zheligovsky, O. M. Podvigina
We study generation of magnetic fields involving large spatial scales by time- and space-periodic small-scale parity-invariant flows. The anisotropic magnetic eddy diffusivity tens…
Numerical evidence of breaking of vortex lines in an ideal fluid
E. A. Kuznetsov, O. M. Podvigina, V. A. Zheligovsky
Emergence of singularity of vorticity at a single point, not related to any symmetry of the initial distribution, has been demonstrated numerically for the first time. Behavior of…
A route to magnetic field reversals: an example of an ABC-forced non-linear dynamo
Olga M. Podvigina
We are investigating numerically the non-linear behavior of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing f…
Dynamo effect in parity-invariant flow with large and moderate separation of scales
V. A. Zheligovsky, O. M. Podvigina, U. Frisch
It is shown that non-helical (more precisely, parity-invariant) flows capable of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity effect are quite common.…