Related papers: Shadowing Lemma and Chaotic Orbit Determination
We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
Three types of orbits are theoretically possible in autonomous Hamiltonian systems with three degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides…
We consider the spectrum of the evolution operator for bound chaotic systems by evaluating its trace. This trace is known to approach unity as $t \rightarrow \infty$ for bound systems. It is written as the Fourier transform of the…
The chaotic or ordered character of orbits in galactic models is an important issue, since it can influence dynamical evolution. This distinction can be achieved with the help of the Smaller Alingment Index - (SALI). We describe here…
The orbits of stars in galaxies are generically chaotic: the chaotic behavior arises in part from the intrinsically grainy nature of a potential that is composed of point masses. Even if the potential is assumed to be smooth, however,…
The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the…
We consider a version of the Vlasov equation on the circle under a periodic potential $V(x,t)$ and a repulsing smooth interaction $W$. We suppose that the Lagrangian for the single particle has chaotic orbits; using Aubry-Mather theory and…
Following Tancredi, Sanchez and Roig (2001)'s criteria of chaos, two ways of setting initial velocities are used in the numerical surveys to explore the possible chaotic and regular orbits for the disc-star-planet systems. We find that the…
Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…
The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
Dynamical friction implies a consistency check on any system where dark matter particles are hypothesised to explain orbital dynamics requiring more mass under Newtonian gravity than is directly detectable. Introducing the assumption of a…
In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…
The paper shows sufficiency conditions for stability of continuous periodic orbits under phase uncertainty. Phase based uncertainty is a trait of bipedal walking robots, where the desired trajectories are parameterized by a monotonous…
We investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. We do this by…
The predictability of weather and climate is strongly state-dependent: special and extremely relevant atmospheric states like blockings are associated with anomalous instability. Indeed, typically, the instability of a chaotic dynamical…
Aims. This paper investigates the chaotic rotation of an oblate satellite in the context of chaos control. Methods. A model of planar oscillations, described with the Beletskii equation, was investigated. The Hamiltonian formalism was…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
According to the standard model of cosmology, the arrangement of matter in the cosmos on scales much larger than galaxies is entirely specified by the initial conditions laid down during inflation. But zooming in by dozens of orders of…