Related papers: Orbit decidability, applications and variations
The goal of this paper is to show there is a single orbit of the c.e. sets with inclusion, $\mathcal{E}$, such that the question of membership in this orbit is $\Sigma^1_1$-complete. This result and proof have a number of nice corollaries:…
Long-distance driving is an important component of planetary surface exploration. Unforeseen events often require human operators to adjust mobility plans, but this approach does not scale and will be insufficient for future missions.…
The motion of astronomical bodies and the centre of mass of the system is not always well perceived by students. One of the struggles is the conceptual change of reference frame, which is the same that held back the acceptance of the…
Based on the doubly special relativity we find a new type of generalized uncertainty principle (GUP) where the coordinate remain unaltered at the high energy while the momentum is deformed at the high energy so that it may be bounded from…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
Relativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a…
We show the existence of a large family of representations supported by the orbit closure of the determinant. However, the validity of our result is based on the validity of the celebrated `Latin Square Conjecture' due to Alon-Tarsi or more…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
In this article, we introduce the notion of good map and use it to establish Gromov-Witten theory for orbifolds.
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
We revisit the quantum de Finetti theorem. We state and prove a couple of variants thereof. In parallel, we introduce an operator version of the Martin boundary on quantum groups and prove generalizations of Biane's theoresm. Our proof of…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…
In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
The increasing volume of space objects in Earth's orbit presents a significant challenge for Space Situational Awareness (SSA). And in particular, accurate orbit prediction is crucial to anticipate the position and velocity of space…
Newton's Theorem of Revolving Orbits derives the force that is necessary to explain a particular precession that leaves the shape of an orbit unchanged. Newton showed that for an orbiting body that is already subject to any central force,…
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…