相关论文: Topological, smooth and holomorphic classification…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…
We study the classification of singularities of holomorphic foliations and non-integrable one-forms under the hypothesis of transversality with real hypersurfaces.
We study a special kind of local invariant sets of singular holomorphic foliations called nodal separators. We define notions of equisingularity and topological equivalence for nodal separators as intrinsic objects and, in analogy with the…
We provide a classification of complex projective surfaces with a holomorphic foliation whose group of birational symetries is infinite.
The study of the recently constructed group foliation for the geopotential forecast equation is continued. The group foliation consists of two systems, namely the automorphic and resolving systems, the analysis of which facilitates the…
This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…
The local classification of conformally flat Lorentzian manifolds with special holonomy groups is obtained. The corresponding local metrics are certain extensions of Riemannian spaces of constant sectional curvature to Walker metrics.
We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…
We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of…
We study conformal structure and topology of leaves of singular foliations by Riemann surfaces.