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On local attraction properties and a stability index for heteroclinic connections
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, weExpand
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Stability and bifurcations of heteroclinic cycles of type Z
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 ofExpand
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On the non-linear stability of the 1:1:1 ABC flow
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 linearlyExpand
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Hopf bifurcation with cubic symmetry and instability of ABC flow
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 atExpand
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Magnetic field generation by convective flows in a plane layer: the dependence on the Prandtl numbers
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 BoussinesqExpand
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The Cauchy-Lagrangian method for numerical analysis of Euler flow
TLDR
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. Expand
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Investigation of the ABC flow instability with application of centre manifold reduction
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 centreExpand
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Simple heteroclinic cycles in R^4
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 symmetryExpand
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Optimal transport by omni-potential flow and cosmological reconstruction
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 equationExpand
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The Monge-Ampère equation: Various forms and numerical solution
TLDR
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. Expand
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