Related papers: Modern light on ancient feud: Robert Hooke and New…
Historically, the discovery of symmetries has played an important role in the progress of our fundamental understanding of nature. This paper will demonstrate that there exists in Newtonian theory in a spherical gravitational field a formal…
In a recent note I argued that the holographic origin of gravitational attraction is the quantum mechanical tendency for operators to grow under time evolution. In a followup the claim was tested in the context of the SYK theory and its…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
Newtonian gravity can be regarded as a hypothetic-deductive system where the inverse square law is the starting point from which gravitational phenomena are deduced. This operational form of presenting gravity endorses problem solving and…
The purpose of this article is to study Newton polygons of certain abelian $L$-functions on curves. Let $X$ be a smooth affine curve over a finite field $\mathbb{F}_q$ and let $\rho:\pi_1(X) \to \mathbb{C}_p^\times$ be a finite character of…
Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…
The principle that celestial bodies must move on circular orbits or on paths resulting from the composition of circular orbits has been assumed as a constant guide in the astronomical thougth of the peoples facing the Mediterranean sea as…
Guided by the Jacobi's work published the year before his death about the rotation of a rigid body, the behavior of the rotation matrix describing the dynamics of the free rigid body is studied. To illustrate this dynamics one draws on a…
In 1956, Bott in his celebrated paper on closed geodesics and Sturm intersection theory, proved an Index Iteration Formula for closed geodesics on Riemannian manifolds. Some years later, Ekeland improved this formula in the case of convex…
Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity,…
It is shown by the author that if gravitons are super-strong interacting particles and the low-temperature graviton background exists, the basic cosmological conjecture about the Dopplerian nature of redshifts may be false. In this case, a…
We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables…
In the 1850s Weierstrass succeeded in solving the Jacobi inversion problem for the hyper-elliptic case, and claimed he was able to solve the general problem. At about the same time Riemann successfully applied the geometric methods that he…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
The textbook-accepted formulation of electromagnetic force was proposed by Lorentz in the 19th century, but its validity has been challenged due to incompatibility with the special relativity and momentum conservation. The Einstein-Laub…
Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a non-existence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign,…
The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some approachable one-parameter families of rational maps; the goal…
Einstein presented the Hole Argument against General Covariance, understood as invariance with respect to a change of coordinates, as a consequence of his initial failure to obtain covariant equations that, in the weak static limit, contain…
A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction…
This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincar\'e and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent…