Related papers: Orbit decidability, applications and variations
The relationship between geometric and variational principles remains central to Nonlinear Analysis. This paper introduces the \textbf{Orbit-Summability Fixed Point Criterion}, a novel, purely dynamical condition, and establishes its…
We present a reduction of the Hilbert-Smith conjecture in the case of the finite dimensional orbit space to some algebraic topology problems.
We prove that for a dynamical system on an algebraic variety over $\overline{\mathbb{Q}}$ generated by finitely many unramified endomorphisms, it is decidable whether a given point has a finite orbit. This is achieved by establishing an…
In previous works, entropic gravity and ungravity have been considered as possible solutions to the dark energy and dark matter problems. To test the viability of these models, modifications to planetary orbits are calculated for ungravity…
This is a comment on `` Is a Circular Orbit Possible According to General Relativity?" by F. T. Hioe and D. Kuebel.
The \emph{Orbit Problem} consists of determining, given a linear transformation $A$ on $\mathbb{Q}^d$, together with vectors $x$ and $y$, whether the orbit of $x$ under repeated applications of $A$ can ever reach $y$. This problem was…
A new generalized St\"ormer problem is proposed. The charged particles motion around a rotating axisymmetric magnetic planet is studied using various conditions mainly in planetary magnetospheres. It is shown that the existence of specific…
In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the…
In this paper, we study the configuration space of orbits, a generalization of the configuration space of points but for algebraic varieties that are acted by an algebraic reductive group. The main objective of this work is to study the…
I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
We discuss the connection between the smooth and metric structure on quotient spaces, prove smoothness of isometries in special cases and discuss an application to a conjecture of Molino.
A unified version of Machado-Bishop theorem in weighted spaces is given. A number of applications illustrate its importance.
In this note, we present an improvement on the large orbit result of Halasi and Podoski, and then answer an open question raised by Chen, Cossey, Lewis, and Tong-Viet.
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
We present a remarkable discretization of the classical Kepler problem which preserves its trajectories and all integrals of motion. The points of any discrete orbit belong to an appropriate continuous trajectory.
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We present a simplified solution to orbit determination of a binary system from astrometric observations. An exact solution was found by Asada, Akasaka and Kasai by assuming no observational errors. We extend the solution considering…