32 citations · 39 across the 8 of their papers we have counts for
9 papers
Normal forms and first integrals of planar maps at elliptic fixed points
Stavros Anastassiou
We study real-analytic, planar, maps, at a neighbourhood of an elliptic fixed point. We construct normal forms for them, when they admit a real-analytic first integral. We prove th…
Detecting invariant manifolds of dynamical systems using persistent homology
Stavros Anastassiou, Žiga Virk
We use methods of Persistent Homology Theory to study invariant manifolds of dynamical systems. We first establish connections between the persistence diagrams of two sets which ar…
Planar vector fields in the kernel of a 1--form
Stavros Anastassiou
We classify, up to a natural equivalence relation, vector fields of the plane which belong to the kernel of a 1--form. This form can be closed, in which case the vector fields are…
Local models for smooth vector fields of the line
Stavros Anastassiou
We present the local classification of singularities of smooth vector fields on the line, with respect to the equivalence relation of --conjugacy. Along the way, we recall the…
Singularities of 3d vector fields preserving the form of Martinet
Stavros Anastassiou
We study the local structure of vector fields on which preserve the Martinet -form . We present the classification of their singularities, up to…
Ancient solutions of the homogeneous Ricci flow on flag manifolds
Stavros Anastassiou, Ioannis Chrysikos
For any flag manifold of a compact simple Lie group we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. Such solutions em…
Darboux polynomials and global phase portraits for the D_2 vector field
Kostas Katsios, Stavros Anastassiou
We study a vector field of R^3 equivariant under the D_2 symmetry group, called "the D_2 field" in the literature. We construct the complete list of Darboux polynomials for it, sol…
Dynamical systems on the Liouville plane and the related strictly contact systems
Stavros Anastassiou
We study vector fields of the plane preserving the form of Liouville. We present their local models up to the natural equivalence relation, and describe local bifurcations of low c…
The Ricci flow approach to homogeneous Einstein metrics on flag manifolds
Stavros Anastassiou, Ioannis Chrysikos
We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a…