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Our motivation for studying this problem is threefold:
(i) When one fixes r = m = 0, the resulting two parameter family is a normal
form for a codimension two bifurcation within the class of planar ...
Phase Portraits of Planar Vector Fields: Computer Proofs
Computer Proofs Planar Vector Fields
2015/8/25
This paper presents an algorithm for computer veri cation of the
global structure of structurally stable planar vector elds. Constructing
analytical proofs for the qualitative properties of phase p...
Periodic Orbits of Vector Fields: Computational Challenges
Computational Challenges Vector Fields
2015/8/25
Simulation of vector elds is ubiquitous: examples occur in every discipline of
science and engineering. Periodic orbits are frequently encountered as trajectories.
We use solutions of initial value...
Reconstruction of vector fields for semi-Lagrangian advection on unstructured, staggered grids
Interpolation Vector fields Unstructured Staggered grids Semi-Lagrangian advection
2015/6/30
Applying the semi-Lagrangian method to discretize the advection of momentum eliminates the Courant number constraint associated with explicit Eulerian momentum advection in coastal ocean models. Key s...
Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Removable singularity divergence Hausdorff measure Hausdorff content Radon measure Frostman’s lemma charges strong charges
2012/6/19
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its v...
Leibniz algebras on symplectic plane and cohomological vector fields
Leibniz algebras symplectic-Poisson geometry anti-cyclic operads Quantum Algebra
2011/9/16
Abstract: By using help of algebraic operad theory, Leibniz algebra theory and symplectic-Poisson geometry are connected. We introduce the notion of cohomological vector field defined on nongraded sym...
Transitive Lie algebras of vector fields---an overview
Transitive Lie algebras vector fields Differential Geometry
2011/9/6
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
A geometric heat flow for vector fields
Geometric heat flow Killing vector fields Yano’s theorem Navier-Stokes equations
2011/9/6
Abstract: This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We s...
On vector fields having properties of Reeb fields
Reeb field presymplectic form contact form geodesible field
2011/9/5
Abstract: We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional mani...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
Spheres with more than 7 vector fields: all the fault of Spin(9)
Spin(9) octonions vector fields on spheres
2011/8/24
Abstract: We give an interpretation in terms of the Lie group Spin(9) of the maximal number of linearly independent vector fields on odd dimensional spheres.
Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds, II
Riemannian Manifolds Killing vector fields Rellich identities
2011/1/21
We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds ad...
A note on proper affine vector fields in Bianchi type IV space-times
Affine vector fields holonomy and decomposability
2010/9/21
Affine vector fields of Bianchi type IV space-times are investigated using holonomy and decomposability, the rank of the 6× 6 Riemann matrix and direct integration technique. From the above study it f...
Complete systems of differential invariants of vector fields in a euclidean space
Vector field Christoffel symbol Bonnet theorem Differential invariant
2010/12/21
The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space Rn is described for groups G=M(n) and G=SM(...