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It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
Numerical integrations of the Solar System have been carried out for decades. Their results have been used, for example, to determine whether the Solar System is chaotic, whether Mercury's orbit is stable, or to help discern Earth's climate…
Direct imaging of exoplanetary systems is a powerful technique that can reveal Jupiter-like planets in wide orbits, can enable detailed characterization of planetary atmospheres, and is a key step towards imaging Earth-like planets. Imaging…
The solar luminosity in the visible changes at the 10-3 level, following an 11 years period. In X-rays, which should not be there, the amplitude varies 100000 times stronger, making their mysterious origin since the discovery in 1938 even…
We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the…
Delta Cir is known as an O7.5 III eclipsing and spectroscopic binary with an eccentric orbit. Penny et al. discovered the presence of a third component in the IUE spectra. The eclipsing binary and the third body revolve around a common…
Ptolemy-s planetary model is an ancient geocentric astronomical model, describing the observed motion of the Sun and the planets. Ptolemy accounted for the deviations of planetary orbits from perfect circles by introducing two small and…
The polar motion data is analyzed to obtain accurate position of the figure axis referred to the Earth-fixed frame. The variation of the figure axis should be the basic object to which the geophysical events are linked. By the method of…
Exploiting the symmetry of the regular icosahedron, Peter Doyle and Curt McMullen constructed a solution to the quintic equation. Their algorithm relied on the dynamics of a certain icosahedral equivariant map for which the icosahedron's…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
The hemispheric asymmetry of the sunspot cycle is a real feature of the Sun. However, its origin is still not well understood. Here we perform nonlinear time series analysis of the sunspot area (and number) asymmetry to explore its…
A regular (i.e., singularity-free) cycling cosmological model is advanced. In the model, there are only two constants: the gravitational constant (or the Planck time) and the cosmic period. The radius of the universe is a simple periodic…
The eccentricity evolution of multiple planet systems can provide valuable constraints on planet formation models. Unfortunately, the inevitable uncertainties in the current orbital elements can lead to significant ambiguities in the nature…
We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
(abbreviated) We use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in eccentric co-planar orbits. We show that the secular dynamics of this system can be described…
In this paper we describe a simple conceptual problem, regarding the actual position of the Sun at sunset or sunrise. Although this problem can be easily explained in terms of rotating frames of references and standard Coriolis Effect, it…
A number of planet-host stars have been observed to rotate with a period equal to an integer multiple of the orbital period of their close planet. We expand this list by analyzing Kepler data of HAT-P-11 and finding a period ratio of 6:1.…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…