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The limited completeness of the Kepler sample for planets with orbital periods $\gtrsim$ 1 yr leaves open the possibility that exoplanetary systems may host undetected giant planets. Should such planets exist, their dynamical interactions…

We have identified more than a hundred close triply eclipsing hierarchical triple star systems from data taken with the space telescope TESS. Many of them have outer periods less than or, close to 100 days, hence, we call them `ultracompact…

Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…

By studying various rational integrable maps on $\mathbf{\hat C}^d$ with $p$ invariants, we show that periodic points form an invariant variety of dimension $\ge p$ for each period, in contrast to the case of nonintegrable maps in which…

Bifurcation cascades in conservative systems are shown to exhibit a generalized diagram, which contains all relevant informations regarding the location of periodic orbits (resonances), their width (island size), irrational tori and the…

The Cepheid Period-Luminosity law is a key rung on the extragalactic distance ladder. However, numerous Cepheids are known to undergo period variations. Monitoring, refining, and understanding these period variations allows us to better…

The majority of extrasolar planets discovered to date have significantly eccentric orbits, some if not all of which may have been produced through planetary migration. During this process, any planets interior to such an orbit would…

We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…

The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective…

Multi-planet systems produce a wealth of information for exoplanet science, but our understanding of planetary architectures is incomplete. Probing these systems further will provide insight into orbital architectures and formation…

We investigate the optimization of dataset weighting in searching for the orbital period of transiting planets when high-precision space-based data with a single transit event are combined with (relatively) low-precision ground-based…

We study theoretical models of three coupled wave guides with a $\mathcal{PT}$-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated…

We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…

For a hypothetical planet on a highly eccentric orbit, we have calculated the osculating orbital parameters and its closest approaches to Earth and Moon over a period of 750 kyr. The approaches which are close enough to influence the…

The phase behaviour of a weakly polydisperse system, such as a colloid with a small spread of particle sizes, can be related perturbatively to that of its monodisperse counterpart. I show how this approach can be generalized to remain…

Context: Distant trans-Neptunian objects are subject to planetary perturbations and galactic tides. The former decrease with the distance, while the latter increase. In the intermediate regime where they have the same order of magnitude…

Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…

We study periodic, piecewise linear maps on the plane starting with the Mort Brown's map. We show that if the number of pieces is two, there is only a short list of possible periods (this fact can be seen as the crystallographic restriction…