Related papers: The Henon Family: The Complex Horseshoe Locus and …
We study those real $\mathcal{C}^\infty$ foliations in complex surfaces whose leaves are holomorphic curves. The main motivation is to try and understand these foliations in neighborhoods of curves: can we expect the space of foliations in…
Based on [1], we study the complexity of horizontality in each twistor space $\hat{E}_{\varepsilon}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over the $2$-torus $T^2$, and obtain…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
Geometrical pictures for the family structure of fundamental particles are developed. They indicate that there might be a relation between the family repetition structure and the number of space dimensions.
There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a…
In this article we provide canonically deformed classical Henon-Heiles system. Further we demonstrate that for proper value of deformation parameter $\theta$ there appears chaos in the model.
The purpose of this paper is to advance the knowledge of the dynamics arising from the creation and subsequent bifurcation of Poincar\'e heteroclinic cycles. The problem is central to dynamics: it has to be addressed if, for instance, one…
Let f:E -> E be a homeomorphism of the plane E. We define open sets P, called {\em pruning fronts} after the work of Cvitanovi\'c, for which it is possible to construct an isotopy H: E x [0,1] -> E with open support contained in the union…
In this paper we consider $C^\infty $-generic families of area-preserving diffeomorphisms of the torus homotopic to the identity and their rotation sets. Let $f_t:\rm{T^2\rightarrow T^2}$ be such a family, $\widetilde{f}_t:\rm…
We define a family of diffeomorphism-invariant models of random connections on principal $G$-bundles over the plane, whose curvatures are concentrated on singular points. In a limit when the number of point grows whilst the singular…
We construct a holomorphically varying family of complex surfaces X_s, parametrized by the points s in any Stein manifold, such that every X_s is a long C^2 which is biholomorphic to C^2 for some but not all values of s.
We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…
We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…
We study the complexity of holomorphic isometries and proper maps from the complex unit ball to type IV classical domains. We investigate on degree estimates of holomorphic isometries and holomorphic maps with minimum target dimension. We…
This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a…
A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical…
We exhibit a family of complex manifolds, which has a member at each odd complex dimension and which has the same cohomology groups as the complex projective space at that dimension, but not homotopy equivalent to it. We also analyze the…
A three-dimensional family of solutions of the Jacobi equations for Poisson systems is characterized. In spite of its general form it is possible the explicit and global determination of its main features, such as the symplectic structure…
A generalized attracting horseshoe is introduced as a new paradigm for describing chaotic strange attractors (of arbitrary finite rank) for smooth and piecewise smooth maps f from Q to Q, where Q is a homeomorph of the unit interval in real…
In this article, we prove that for several one-dimensional holomorphic families of holomorphic maps, in the parameter plane, there exists a local piece of a curve that lands at a given parabolic parameter, in the spirit of well-known…