Related papers: Analysis of Round Off Errors with Reversibility Te…
We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…
Calculating the long term solution of ordinary differential equations, such as those of the $N$-body problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally…
Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
We study the dynamics of the space debris in regions corresponding to minor resonances; precisely, we consider the resonances 3:1, 3:2, 4:1, 4:3, 5:1, 5:2, 5:3, 5:4, where a j:l resonance (with j, l integers) means that the periods of…
Detumbling refers to the act of dampening the angular velocity of the satellite. This operation is of paramount importance since it is virtually impossible to nominally perform any other operation without some degree of attitude control.…
Peebles (1989) showed that in the gravitational instability picture galaxy orbits can be traced back in time from a knowledge of their current positions, via a variational principle. We modify this variational principle so that galaxy…
Hamiltonian trajectories are strictly time-reversible. Any time series of Hamiltonian coordinates {q} satisfying Hamilton's motion equations will likewise satisfy them when played "backwards", with the corresponding momenta changing signs :…
The important phenomenon of "stickiness" of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as classical and statistical mechanics,…
This article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits. In addition, tangencies in the intersection of un/stable manifolds are…
We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately…
We consider a class of models describing the dynamics of $N$ Boolean variables, where the time evolution of each depends on the values of $K$ of the other variables. Previous work has considered models with dissipative dynamics. Here we…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
The understanding of non-linear effects in circular storage rings and colliders based on superconducting magnets is a key issue for the luminosity the beam lifetime optimisation. A detailed analysis of the multidimensional phase space…
A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method (PRL 78, 4733 (1997)) is developed. This approach provides a classification of the set of transformations necessary…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
It is shown how the violation of the invariance of the $Z$-component of the orbital angular momentum $L_z$ in the axially symmetric potential of the Galaxy with a bar can serve as an indicator of the degree of orbital chaos of globular…
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a…
Probabilistic rounding error analysis can yield much sharper bounds than classical worst-case theory, but existing results typically rely on zero-mean rounding errors and often leave the confidence parameter implicit. This work revisits…