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Publications Influence

On local attraction properties and a stability index for heteroclinic connections

- O. Podvigina, P. Ashwin
- Mathematics, Physics
- 18 August 2010

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 with a basin of attraction N, we… Expand

39 6- PDF

Stability and bifurcations of heteroclinic cycles of type Z

- O. Podvigina
- Mathematics, Physics
- 21 August 2011

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 properties of a class of… Expand

25 4- PDF

On the non-linear stability of the 1:1:1 ABC flow

- O. Podvigina, A. Pouquet
- Mathematics
- 15 August 1994

Abstract ABC flows which can be considered as prototypes for the study of the onset of three-dimensional spatio-temporal turbulence are known both analytically and numerically to be linearly… Expand

52 3

Hopf bifurcation with cubic symmetry and instability of ABC flow

- P. Ashwin, O. Podvigina
- Mathematics
- Proceedings of the Royal Society of London…
- 8 July 2003

We examine the dynamics of generic Hopf bifurcation in a system that is symmetric under the action of the rotational symmetries of the cube. We classify the generic branches of periodic solutions at… Expand

30 3- PDF

Magnetic field generation by convective flows in a plane layer: the dependence on the Prandtl numbers

- O. Podvigina
- Physics
- 1 August 2008

Investigation of magnetic field generation by convective flows is carried out for three values of kinematic Prandtl number: P = 0.3, 1 and 6.8. We consider Rayleigh–Bénard convection in Boussinesq… Expand

10 3

The Cauchy-Lagrangian method for numerical analysis of Euler flow

- O. Podvigina, V. Zheligovsky, U. Frisch
- Mathematics, Computer Science
- J. Comput. Phys.
- 20 April 2015

TLDR

12 1- PDF

Investigation of the ABC flow instability with application of centre manifold reduction

- O. Podvigina
- Mathematics
- 1 June 2006

We demonstrate that application of a generalized centre manifold is advantageous when low-dimensional reductions of continuous dynamical systems of hydrodynamic type are considered. The centre… Expand

4 1

Simple heteroclinic cycles in R^4

- O. Podvigina, P. Chossat
- Mathematics, Physics
- 1 October 2013

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 action of a symmetry… Expand

12 1- PDF

Optimal transport by omni-potential flow and cosmological reconstruction

- U. Frisch, O. Podvigina, B. Villone, V. Zheligovsky
- Mathematics, Physics
- 10 November 2011

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 inviscid Burgers equation… Expand

5 1- PDF

The Monge-Ampère equation: Various forms and numerical solution

- V. Zheligovsky, O. Podvigina, U. Frisch
- Mathematics, Physics
- J. Comput. Phys.
- 7 October 2009

TLDR

22- PDF

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