Related papers: Identifying Fixed Points in the Three-Body Problem…
The existence of stable periodic orbits and chaotic invariant sets of singularly perturbed problems of fast-slow type having Bogdanov-Takens bifurcation points in its fast subsystem is proved by means of the geometric singular perturbation…
Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…
We report the first definitive experimental observation of periodic orbits (POs) in the spectral properties of an elastodynamic system. The Fourier transform of the density of flexural modes show peaks that correspond to stable and unstable…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
This paper introduces the Circular Restricted n-Body Problem (CRNBP), an extension of the bicircular restricted four-body problem (BCR4BP) designed to describe the dynamics of an n-body system. In the CRNBP, each massive body in the system…
The Team Orienteering Problem (TOP) is an attractive variant of the Vehicle Routing Problem (VRP). The aim is to select customers and at the same time organize the visits for a vehicle fleet so as to maximize the collected profits and…
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…
A gravitational close encounter of a small body with a planet may produce a substantial change of its orbital parameters which can be studied using the circular restricted three-body problem. In this paper we provide parametric…
The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is…
This paper investigates the distributed fixed point finding problem for a global operator over a directed and unbalanced multi-agent network, where the global operator is quasinonexpansive and only partially accessible to each individual…
A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for…
We present a method for establishing invariant manifolds for saddle--center fixed points. The method is based on cone conditions, suitably formulated to allow for application in computer assisted proofs, and does not require rigorous…
Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…
By employing a unified state-space design framework, this paper proposes a novel systematic analysis and synthesis method that facilitates the implementation of both conventional zero-order (ZO) and high-order (HO) DObs. Furthermore, this…
The relaxed optimal $k$-thresholding pursuit (ROTP) is a recent algorithm for linear inverse problems. This algorithm is based on the optimal $k$-thresholding technique which performs vector thresholding and error metric reduction…
The current series of two papers focus on a 3-dimensional Lotka-Volterra competition model of differential equations with seasonal succession, which exhibits that populations experience an external periodically forced environment. We are…
It is well known that finding a global optimum is extremely challenging for nonconvex optimization. There are some recent efforts \cite{anandkumar2016efficient, cartis2018second, cartis2020sharp, chen2019high} regarding the optimization…
Since Poincar\'e, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at…