相关论文: A proof of Bertrand's theorem using the theory of …

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…

K.T. Chen showed that iterated integrals give comparison isomorphisms between the cohomologies of bar complexes and fundamental group rings. This led to the development of an algebraic-geometric approach to studying periods given by…

We give here a simple proof of the centrality of the congruence subgroup kernel in the higher rank isotropic case.

In this article, using an infinite-dimensional equivariant Conley index, we prove a generalization of the profitable Liapunov center theorem for symmetric potentials. Consider the system $\ddot{q}= -\nabla U(q),$ where $U(q)$ is a…

We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are…

The main result of this paper is an analogue for a continuous family of tori of Kronecker-Weyl's unique ergodicity of irrational rotations. We show that the notion corresponding in this setup to irrationality, namely asynchronicity, is…

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

We provide a rigorous proof of the CPT theorem within the framework of 'Lagrangian' quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches within the Lagrangian…

We present a variation of the proof in the first author's "Mob families and mad families" of Con(b<a), which in particular removes some of the obstacles to generalising the argument to uncountable cardinals.

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

We give a new proof of Lucas' Theorem in elementary number theory.

We use motivic methods to give a quick proof of Berthelot's conjecture stating that the push-forward map in rigid cohomology of the structural sheaf along a smooth and proper map has a canonical structure of overconvergent F-isocrystal on…

Fix an irrational number $\alpha$, and consider a random walk on the circle in which at each step one moves to $x+\alpha$ or $x-\alpha$ with probabilities $1/2, 1/2$ provided the current position is $x$. If an observable is given we can…

The central limit theorem for Markov chains generated by iterated function systems consisting of orientation preserving homeomorphisms of the interval is proved. We study also ergodicity of such systems.

It was proved recently that the correlation functions of a semi-simple cohomological field theory satisfy the so called Eynard--Orantin topological recursion. We prove that in the settings of singularity theory, the relations can be…

We survey the classical results of the Dirichlet Approximation Theorem.

An equivalent but useful version on the Homological Nerve Theorem is proved.

We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $$\dot x=-y+A(x,y),\;\dot y=x+B(x,y),$$ where $A,\;B\in \mathbb{R}[x,y]$, which can be reduced to the Li\'enard type equation. When $deg(A)\leq 4$ and $deg(B) \leq 4$,…