Related papers: Grand orbit relations in wandering domains
The discovery of over 200 extrasolar planets with the radial velocity (RV) technique has revealed that many giant planets have large eccentricities, in striking contrast with most of the planets in the solar system and prior theories of…
In this article we study orbits of proximal pairs in almost automorphic subshifts. The corresponding orbits in the maximal equicontinuous factor are precisely those orbits that intersect the boundary of the subshift's separating cover. We…
Context: The discovery of distant trans-Neptunian objects has led to heated discussions about the structure of the outer Solar System. Aims: We study the dynamical evolution of small bodies from the Hill regions of migrating giant gaseous…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
Short-period super-Earths and mini-Neptunes encircle more than $\sim50\%$ of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to…
This paper concerns the asymptotic expansion of the solution of the Dirichlet-Laplace problem in a domain with small inclusions. This problem is well understood for the Neumann condition in dimension greater than two or Dirichlet condition…
The Fatou-Julia iteration theory of rational and transcendental entire functions has recently been extended to quasiregular maps in more than two real dimensions. Our goal in this paper is similar; we extend the iteration theory of analytic…
This paper studies the geometry of Fatou components in non-Archimedean dynamics. By explicitly computing a wandering domain constructed by Benedetto, it provides the first example of a Fatou component that is an irrational disk.
Special exotic class of dynamical systems~ -- the implicit maps~ -- is considered. Such maps, particularly, can appear as a result of using of implicit and semi-implicit iterative numerical methods. In the present work we propose the…
The detection of exoplanets through direct imaging has produced numerous new positive identifications in recent years. The technique is biased towards planets at wide separations due to the difficulty in removing the stellar signature at…
Suppose that $f$ is a transcendental entire function, $V \subsetneq \mathbb{C}$ is a simply connected domain, and $U$ is a connected component of $f^{-1}(V)$. Using Riemann maps, we associate the map $f \colon U \to V$ to an inner function…
Let $f:\mathbb C\to \widehat{\mathbb C}=\mathbb C \cup\{\infty\}$ be a transcendental meromorphic function (possibly without any pole) with a single essential singularity, and that is chosen to be at $\infty$. The set of points…
Numerical modeling of the interaction of giant planets and the planetesimal disk was carried out for the Nice model, in which the initial orbits of the planets are in resonant configurations. In addition to the standard Nice model,…
We prove new unconditional results of sparsity of integral points on orbits under many maps and correspondences in arbitrary dimensions, generalizing theorems of Yasufuku(2015) and others. The main ingredients are new diophantine…
We describe a topological mechanism for the existence of diffusing orbits in a dynamical system satisfying the following assumptions: (i) the phase space contains a normally hyperbolic invariant manifold diffeomorphic to a two-dimensional…
As gas giant planets evolve, they may scatter other planets far from their original orbits to produce hot Jupiters or rogue planets that are not gravitationally bound to any star. Here, we consider planets cast out to large orbital…
We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and…
The NASA Kepler and K2 Missions have recently revealed a population of transiting giant planets orbiting moderately evolved, low-luminosity red giant branch stars. Here, we present radial velocity measurements of three of these systems,…
Understanding the dominant brown dwarf and giant planet formation processes, and finding out whether these processes rely on completely different mechanisms or share common channels represents one of the major challenges of astronomy and…
Several celestial bodies in co-orbital configurations exist in the solar system. However, co-orbital exoplanets have not yet been discovered. This lack may result from a degeneracy between the signal induced by co-orbital planets and other…