Related papers: A note on larger orbit size

In this letter, we revisit the {\em orbit problem}, which was studied in \cite{HAR69,SHA79,KL86}. In \cite{KL86}, Kannan and Lipton proved that this problem is decidable in polynomial time. In this paper, we study the {\em approximate orbit…

We present the notion of orbit decidability into a more general framework, exploring interesting generalizations and variations of this algorithmic problem. A recent theorem by Bogopolski-Martino-Ventura gave a renovated protagonism to this…

This note is the follow up to a paper by M. Waldschmidt.

Reply to a comment by T. Rakovszky, F. Pollmann, and C. W von Keyserlingk [arXiv:2010.07969].

We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close.…

We explore the distant giant planet hypothesis by integrating the large semi-major axis, large pericenter Trans-Neptunian Objects (TNOs) in the presence of the giant planets and an external perturber whose orbit is consistent with the…

We give a negative answer to a question by J.M. Landsberg on the nature of normalizations of orbit closures. A counterexample originates from the study of complex, ternary, cubic forms.

These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…

This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…

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…

In this note the authors have raised the question regarding the validity of the main result in [1] by setting an example.

A minor improvement is made to the calculation of the inhomogeneity term. The new calculation gives better agreement with the observations of Daoud et al. and Cheng-Graessley-Melnichenko.

The note complements topological aspects of the theory of chiral algebras.

This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…

We prove an effective version of a result obtained recently by Kleinbock and Weiss on equidistribution of expanding translates of orbits of horospherical subgroups in the space of lattices.

Construction of a theory of orbits about a precessing oblate planet, in terms of osculating elements defined in a frame of the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2005, 2006). We now combine that…

We provide a variety of cases in which two factorizations have Hurwitz orbits of the same size. We begin with prototypical results about factorizations of length two, and show that cycling elements or flipping and inverting elements in any…

Discretely self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field for large discretely self-similar initial data are constructed in this note, extending the construction of Brandolese and Karch…

As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey…

We use astrometry of Pluto and other TNOs to constrain the sky location, distance, and mass of the possible additional planet (Planet Nine) hypothesized by Batygin and Brown (2016). We find that over broad regions of the sky, the inclusion…