Related papers: $\infty$-jets of difeomorphisms preserving orbits …

The main result of this paper is that every non-trivial Hamiltonian diffeomorphism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S^2 provided the…

We generalize the main result of Demailly \cite{D2} for the bundles $E_{k,m}^{GG}(V^*)$ of jet differentials of order $k$ and weighted degree $m$ to the bundles $E_{k,m}(V^*)$ of the invariant jet differentials of order $k$ and weighted…

In this paper we study holomorphic vector bundles with singular Hermitian metrics whose curvature are Hermitian matrix currents. We obtain an extension theorem for holomorphic jet sections of nef holomorphic vector bundle on compact…

We first study the dynamics of the geodesic flow of a meromorphic connection on a Riemann surface, and prove a Poincar\'e-Bendixson theorem describing recurrence properties and $\omega$-limit sets of geodesics for a meromorphic connection…

Let $(\mathrm{M}, \omega_{0})$ be a connected paracompact smooth oriented manifold. We establish a necessary and sufficient conditions on Lie subalgebra $\mathfrak{a}$ of $\mathrm{T M}$ such that its orbits becomes diffeomorphic to an open…

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field)…

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…

In the theory of surface diffeomorphisms relative to homoclinic and heteroclinic orbits, it is possible to compute a one-dimensional representative map for any irreducible isotopy class. The topological entropy of this graph representative…

We study a special kind of singular vorticities in ideal 2D fluids that combine features of point vortices and vortex sheets, namely pointed vortex loops. We focus on the coadjoint orbits of the area-preserving diffeomorphism group of…

We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\mathbb{k}$ of characteristic $0$. That is, if $\Phi\colon G\longrightarrow G$…

The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\to E\to M$, it is shown that integrable multivector fields in $E$ are equivalent to integrable connections in the bundle $E\to…

Two flows on a finite-dimensional normed space $X$ are equivalent if some homeomorphism $h$ of $X$ preserves all orbits, i.e., $h$ maps each orbit onto an orbit. Under the assumption that $h$, $h^{-1}$ both are $\beta$-H\"{o}lder continuous…

We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / \Gamma$, where $G$ is a complex connected Lie group and $\Gamma$ is a cocompact lattice in it. The main result proved here is a structure…

In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that…

We prove that every homomorphism $\mathcal{O}^E_\zeta\to\mathcal{O}^F_\zeta$, with $E$ and $F$ Banach spaces and $\zeta\in\mathbb{C}^m$, is induced by a $\mathop{\mathrm{Hom}}(E,F)$-valued holomorphic germ, provided that $1\leq m<\infty$. A…

Let $\mathbb{K}$ be an algebraically closed field of characteristic zero, and $V$ a hypersurface defined by an irreducible polynomial $f$ with coefficients in $\mathbb{K}$ . In this article we prove that an Embedded Deformation of $V$ which…

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…

Let $f:T^2\to\mathbb{R}$ be a Morse function on $2$-torus $T^2$ such that its Kronrod-Reeb graph $\Gamma(f)$ has exactly one cycle, i.e. it is homotopy equivalent to $S^1$. Under some additional conditions we describe a homotopy type of the…

Extending the work of the first author, we introduce a notion of semisimple topological field theory in arbitrary even dimension and show that such field theories necessarily lead to stable diffeomorphism invariants. The main result of this…

In this paper, we investigate vector fields on polyhedral complexes and their associated trajectories. We study vector fields which are analogue of the gradient vector field of a function in the smooth case. Our goal is to define a nice…