Chaotic Entanglement: Entropy and Geometry

In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that exhibits several properties consistent with quantum entanglement. In such a state, the chaotic behavior of each system is stabilized onto one of the system’s many unstable periodic orbits (generally located densely on the associated attractor), and the ensuing periodicity of each system is sustained by the symbolic dynamics of its partner system, and vice versa. Notably, chaotic entanglement is an entropy-reversing event: the entropy of each member of an entangled pair decreases to zero when each system collapses onto a given period orbit. In this paper, we discuss the role that entropy plays in chaotic entanglement. We also describe the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved patterns. We conclude with a discussion of future research directions.

Discovery of β Cep pulsations in the eclipsing binary V453 Cygni

ABSTRACT V453 Cyg is an eclipsing binary containing 14 and 11 $\, {\rm M}_\odot$ stars in an eccentric short-period orbit. We have discovered β Cep-type pulsations in this system using Transiting Exoplanet Survey Satellite data. We identify seven significant pulsation frequencies, between 2.37 and 10.51 d−1, in the primary star. These include six frequencies that are separated by yet significantly offset from harmonics of the orbital frequency, indicating they are tidally perturbed modes. We have determined the physical properties of the system to high precision: V453 Cyg A is the first β Cep pulsator with a precise mass measurement. The system is a vital tracer of the physical processes that govern the evolution of massive single and binary stars.

On the secondary’s rotation in a synchronous binary asteroid

ABSTRACT This article studies the secondary’s rotation in a synchronous binary asteroid system in which the secondary enters the 1:1 spin-orbit resonance. The model used is the planar full two-body problem, composed of a spherical primary plus a triaxial ellipsoid secondary. Compared with classical spin-orbit work, there are two differences: (1) influence of the secondary’s rotation on the mutual orbit is considered and (2) instead of the Hamiltonian approach, the approach of periodic orbits is adopted. Our studies find the following. (1) The genealogy of the two families of periodic orbits is the same as that of the families around triangular libration points in the restricted three-body problem. That is, the long-period family terminates on to a short-period orbit travelling N times. (2) In the limiting case where the secondary’s mass is negligible, our results can be reduced to classical spin-orbit theory, by equating the long-period orbit with free libration and the short-period orbit with the forced libration caused by orbit eccentricity. However, the two models show obvious differences when the secondary’s mass is non-negligible. (3) By studying the stability of periodic orbits for a specific binary asteroid system, we are able to obtain the maximum libration amplitude of the secondary (which is usually less than 90°) and the maximum mutual orbit eccentricity that does not break the secondary’s synchronous state. We also find an anti-correlation between the secondary’s libration amplitude and the orbit eccentricity. The (65803) Didymos system is taken as an example to show the results.

An ultra-short period rocky super-Earth orbiting the G2-star HD 80653

Ultra-short period (USP) planets are a class of exoplanets with periods shorter than one day. The origin of this sub-population of planets is still unclear, with different formation scenarios highly dependent on the composition of the USP planets. A better understanding of this class of exoplanets will, therefore, require an increase in the sample of such planets that have accurate and precise masses and radii, which also includes estimates of the level of irradiation and information about possible companions. Here we report a detailed characterization of a USP planet around the solar-type star HD 80653 ≡EP 251279430 using the K2 light curve and 108 precise radial velocities obtained with the HARPS-N spectrograph, installed on the Telescopio Nazionale Galileo. From the K2 C16 data, we found one super-Earth planet (Rb = 1.613 ± 0.071 R⊕) transiting the star on a short-period orbit (Pb = 0.719573 ± 0.000021 d). From our radial velocity measurements, we constrained the mass of HD 80653 b to Mb = 5.60 ± 0.43 M⊕. We also detected a clear long-term trend in the radial velocity data. We derived the fundamental stellar parameters and determined a radius of R⋆ = 1.22 ± 0.01 R⊙ and mass of M⋆ = 1.18 ± 0.04 M⊙, suggesting that HD 80653 has an age of 2.7 ± 1.2 Gyr. The bulk density (ρb = 7.4 ± 1.1 g cm−3) of the planet is consistent with an Earth-like composition of rock and iron with no thick atmosphere. Our analysis of the K2 photometry also suggests hints of a shallow secondary eclipse with a depth of 8.1 ± 3.7 ppm. Flux variations along the orbital phase are consistent with zero. The most important contribution might come from the day-side thermal emission from the surface of the planet at T ~ 3480 K.

The hazard from fragmenting comets

Comet disintegration proceeds both through sublimation and discrete splitting events. The cross-sectional area of material ejected by a comet may, within days, become many times greater than that of the Earth, making encounters with such debris much more likely than collisions with the nucleus itself. The hierarchic fragmentation and sublimation of a large comet in a short period orbit may yield many hundreds of such short-lived clusters. We model this evolution with a view to assessing the probability of an encounter which might have significant terrestrial effects, through atmospheric dusting or multiple impacts. Such an encounter may have contributed to the large animal extinctions and sudden climatic cooling of 12,900 years ago, and the near-simultaneous collapse of civilisations around 2350 BC.

Hidden Hyperchaotic Attractors in a Modified Lorenz–Stenflo System with Only One Stable Equilibrium

This paper reports the finding of a four-dimensional (4D) non-Sil'nikov autonomous system with three quadratic nonlinearities, which exhibits some behavior previously unobserved: hidden hyperchaotic attractors with only one stable equilibrium. The algebraical form of the non-Sil'nikov chaotic attractor is very similar to the hyperchaotic Lorenz–Stenflo system but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact this system has only one stable equilibrium, but can exhibit hidden hyperchaos, chaos, periodic orbit. Moreover, the coexistence of attracting sets can be obtained in the system for some parameter values and different initial conditions, such as hyperchaotic attractor and point, hyperchaotic attractor and period orbit. To further analyze the new system, the ultimate bound and positively invariant set for the modified hyperchaotic Lorenz–Stenflo system are also obtained. Moreover, the complete mathematical characterizations for 4D Hopf bifurcation are rigorously derived and studied.

Research on Chaotic Orbit in Mandelbrot Set

In this paper, the chaotic orbit in Mandelbrot set is introduced. On the basis of other scholars research, the character and distribution rules of pre-periodic orbits and pre-periodic points-Misiurewiz points about Mandelbrot set chaos-fractal images were studied. The software of constructing the general M-J set with Java Applet is improved. Using the method of computer mathematic experiments, the paper analyses the fixed orbit and period orbit in the M-set, gains the topology relationship of M set in super stable points, a recurrence formula between the period orbit and M-set periodic-buds is created.