Related papers: The stabilized symplectic embedding problem for po…
In previous work, the second author and M\"uller determined the function $c(a)$ giving the smallest dilate of the polydisc $P(1,1)$ into which the ellipsoid $E(1,a)$ symplectically embeds. We determine the function of two variables $c_b(a)$…
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…
We study symplectic embeddings of ellipsoids into balls. In the main construction, we show that a given embedding of 2m-dimensional ellipsoids can be suspended to embeddings of ellipsoids in any higher dimension. In dimension 6,s if the…
In the present article, we further investigate the properties of squeezing function corresponding to polydisk. We work out some explicit expressions of squeezing function corresponding to polydisk.
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…
We establish various stability results for symplectic surfaces in symplectic $4-$manifolds with $b^+=1$. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify…
This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
In any dimension $2n \ge 6$ we show that certain spaces of symplectic embeddings of a polydisk into a product $B^4 \times \Bbb R^{2(n-2)}$ of a $4$-ball and Euclidean space, are not path connected. We also show that any pair of such…
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region…
We consider the embedding function $c_b(a)$ describing the problem of symplectically embedding an ellipsoid $E(1,a)$ into the smallest possible scaling by $\lambda>1$ of the polydisc $P(1,b)$. In particular, we calculate rigid-flexible…
The steady-state structure of self-gravitating, magnetized accretion disks is studied using a set of self-similar solutions which are appropriate in the outer regions. The disk is assumed to be isothermal and the magnetic field outside of…
In this paper we provide the stability of generic polycycles of hybrid planar vector fields, extending previous known results in the literature. The polycycles considered here may have hyperbolic saddles, tangential singularities and jump…
We consider discrete ensembles of linear, scalar control systems with single-inputs. Assuming that all the individual systems are unstable, we investigate whether there exist linear feedback control laws that can asymptotically stabilize…
Let $(X, H)$ be a polarized smooth projective algebraic surface and $E$ is globally generated, stable vector bundle on $X$. Then the Syzygy bundle $M_E$ associated to it is defined as the kernel bundle corresponding to the evaluation map.…
This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…