相关论文: Dynamics of birational plane mappings. The Arnold …

This paper deals with holomorphic self-maps of the complex projective plane and the algebraic relations among the eigenvalues of the derivatives at the fixed points. These eigenvalues are constrained by certain index theorems such as the…

We define a graded multiplication on the vector space of essential paths on a graph $G$ (a tree) and show that it is associative. In most interesting applications, this tree is an ADE Dynkin diagram. The vector space of length preserving…

Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…

This paper is a continuation of the paper [5] dealing with dynamics of dianalytic transformations of nonorientable Klein surfaces. We are examining mainly the transformations of the real projective plane $P^{2}, $ whose orientable double…

Let K be the field of fractions of a Henselian discrete valuation ring O_K. Let X_K/K be a smooth proper geometrically connected scheme admitting a regular model X/O_K. We show that the index \delta(X_K/K) of X_K/K can be explicitly…

Let $k$ be an arbitrary field, and C be a curve in A^n defined parametrically by x_1=f_1(t),...,x_n=f_n(t), where f_1,...,f_n\in k[t]. A necessary and sufficient condition for the two function fields k(t) and k(f_1,...,f_n) to be same is…

This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…

By integrating curvatures multiplied non-trivial densities, we introduce an integral expression of the Arnold strangeness that is a celebrated plane curve invariant. The key is a partition function by Shumakovitch to reformulate Arnold…

We consider discrete dynamical systems obtained as deformations of mutations in cluster algebras associated with finite-dimensional simple Lie algebras. The original (undeformed) dynamical systems provide the simplest examples of…

We study asymptotics of the spectral measure of a randomly chosen partial automorphism of a rooted tree. To every partial automorphism $x$ we assign its action matrix $A_x$. It is shown that the uniform distribution on eigenvalues of $A_x$…

The natural forms of the Leibniz rule for the $k$th derivative of a product and of Fa\`a di Bruno's formula for the $k$th derivative of a composition involve the differential operator $\partial^k/\partial x_1 ... \partial x_k$ rather than…

We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…

Two theorems witnessing the abundance of geometrically trivial strongly minimal autonomous differential equations of arbitrary order are shown. The first one states that a generic algebraic vector field of degree $d\geq 2$ on the affine…

We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…

The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of ``observables'' for general relativity. Recent work of Chamseddine and Connes suggests that…

Let $T$ be a $C^{1}$ competitive map on a rectangular region $R\subset \mathbb{R}^{2}$. The main results of this paper give conditions which guarantee the existence of an invariant curve $C$, which is the graph of a continuous increasing…

In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…

Let P2(Rd) be the space of probability measures on Rd with finite second moment. The path independence of additive functionals of McKean-Vlasov SDEs is characterized by PDEs on the product space Rd*P2(Rd) equipped with the usual derivative…

For relatively form-compact perturbations of non-negative selfadjoint operators, we obtain an upper bound on the number of discrete eigenvalues in half-planes separated from the positive real axis. The bound is given in terms of a partial…

We consider the real dynamics of a two parameter family of plane birational maps, focusing especially on an open subset of parameter space on which the real and complex dynamics are in close agreement. On the complex side, we find a…