Related papers: Fundamental limits from chaos on instability time …
We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking…
Using an innovative damped-Newton method, we report the first calculation of many distinct unstable periodic orbits (UPOs) of a large high-dimensional extensively chaotic partial differential equation. A majority of the UPOs turn out to be…
Many of the multi-planet systems discovered to date have been notable for their compactness, with neighbouring planets closer together than any in the Solar System. Interestingly, planet-hosting stars have a wide range of ages, suggesting…
The high-multiplicity exoplanet systems are generally more tightly packed when compared to the solar system. Such compact multi-planet systems are often susceptible to dynamical instability. We investigate the impact of dynamical…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a…
Transient instability in nonlinear stochastic dynamical systems is a fundamental limitation in safety-critical aerospace applications, particularly during powered descent and landing where failure is driven by finite-time excursions rather…
We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as…
The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the…
The observed average lifetime of the population of star clusters in the Solar Neighbourhood, the Small Magellanic Cloud and in selected regions of M51 and M33 is compared with simple theoretical predictions and with the results of N-body…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
Chaotic instability in many-body systems is commonly quantified by the largest Lyapunov exponent, yet general constraints on its magnitude in classical interacting systems remain poorly understood. Here we establish explicit,…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of…
Fragmentation of a spiral arm is thought to drive the formation of giant clumps in galaxies. Using linear perturbation analysis for self-gravitating spiral arms, we derive an instability parameter and define the conditions for clump…
We analyze the orbital dynamics of spherical test bodies in ``black hole surrounded by dark matter halo'' spherically symmetric spacetimes. When the test body pulsates periodically (such as a variable star), altering its quadrupole tensor,…
Planet formation simulations consistently predict compact systems of numerous small planets in chains of mean motion resonances formed by planet-disk interaction, but transiting planet surveys have found most systems to be non-resonant and…
We present a parameter study of the possibility of tidally triggered disk instability. Using a restricted N-body model which allows for a survey of an extended parameter space, we show that a passing dwarf star with a mass between 0.1 and 1…
Uncertainty in the initial conditions of dynamical systems can cause exponentially fast divergence of trajectories, a signature of deterministic chaos. Here, we derive a classical uncertainty relation that sets a speed limit on the rates of…
We consider spatiotemporal chaotic systems for which spatial correlation functions decay substantially over a length scale xi (the spatial correlation length) that is small compared to the system size L. Numerical simulations suggest that…