Related papers: A Hasse Principle for Periodic Points

A palindromic periodicity is a factor of an infinite word $(ps)^\omega$ where $p$ and $s$ are palindromes and the factor has length at least $|ps|$, for example, $accabaccab$. In this paper we describe several ways in which a palindromic…

We give sufficient conditions under which the set of eventually periodic points in the intersection of immediate attracting basins boundaries is non-empty. We give other conditions under which this set is dense in the intersection.

In nonstandard analysis, Fehrele's principle is a beautiful criterion for a set to be internal, stating that every galactic halic set is internal. In this note, we use this principle to prove some well-known results in topology, including…

We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that…

I aim to clarify the physical content and significance of naturalness. Physicists' earliest understanding of naturalness, as an autonomy of scales (AoS) requirement provides the most cogent definition of naturalness and I will assert that…

We study absolutely periodic points and trajectories of Hamiltonian systems. Our main result is a necessary and sufficient for a Hamiltonian system to have the following property: if there exists one absolutely periodic trajectory then all…

For any nonzero $h\in\mathbb{Z}$, we prove that a positive proportion of integral binary cubic forms $F$ do locally everywhere represent $h$ but do not globally represent $h$; that is, a positive proportion of cubic Thue equations…

Let $K$ be the function field of a $p$-adic curve, $G$ a semisimple simply connected group over $K$ and $X$ a $G$-torsor over $K$. A conjecture of Colliot-Th\'el\`ene, Parimala and Suresh predicts that if for every discrete valuation $v$ of…

Fix $n\ge3$. For the pure field $K_a=\mathbb Q(\theta)$ with $\theta^n=a$, where $a\neq \pm 1$ is $n$th-power-free, we encode an integral basis in the fixed coordinate $\{1,\theta,\dots,\theta^{n-1}\}$ by its \emph{shape}. We prove a sharp…

We prove that a $C^{\infty}$-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem…

The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…

The current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains. We first prove the global existence and boundedness of…

We derive the Hasse principle and weak approximation for pencils of certain varieties in the spirit of work by Colliot-Th\'el\`ene,Sansuc and Harpaz-Skorobogatov-Wittenberg. Our varieties are defined through polynomials in many variables…

Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.

We investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit converges to a periodic orbit and, moreover, that there exists…

In rotor walk on a finite directed graph, the exits from each vertex follow a prescribed periodic sequence. Here we consider the case of rotor walk where a particle starts from a designated source vertex and continues until it hits a…

We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the…

Recently, an approach for metallic superlattices based on the finite periodic systems theory was introduced \cite{Pereyra2020}. Unlike most, if not all, of the published approaches that are valid in the $n \rightarrow \infty $ limit, the…

Fix an odd prime $p$. If $r$ is a positive integer and $f$ a polynomial with coefficients in $\mathbb{F}_{p^r}$, let $P_{p,r}(f)$ be the proportion of $\mathbb{P}^1(\mathbb{F}_{p^r})$ that is periodic with respect to $f$. We show that as…

The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this…