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The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two-dimensional, quasi-geostrophic, incompressible fluid.
We consider a natural Lagrangian system defined on a complete Riemannian manifold being subjected to action of a time-periodic force field with potential U(q, t, ε) = f(εt)V(q) depending slowly on time. It is assumed that the factor f(τ) is periodic and vanishes at least at one point on the...
We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the...
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in S
2. This isomorphism converts the original quadratures into elliptic integrals and...
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the...
A generalized model with bifurcations associated with blue sky catastrophes is introduced. Depending on an integer index m, different kinds of attractors arise, including those associated with quasi-periodic oscillations and with hyperbolic chaos. Verification of the hyperbolicity is provided...
Chow and Lou  showed in 2003 that under certain conditions the combinatorial analogue of the Hamilton Ricci flow on surfaces converges to Thruston’s circle packing metric of constant curvature. The combinatorial setting includes weights defined for edges of a triangulation. A crucial...
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