Related papers: Efficient manifold tracing for planar maps
Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…
Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…
Continuum robots (CR) offer excellent dexterity and compliance in contrast to rigid-link robots, making them suitable for navigating through, and interacting with, confined environments. However, the study of path planning for CRs while…
This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly,…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…
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…
Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs on the slow time scale are a prominent feature of slow-fast…
Precise radial velocity measurements have led to the discovery of ~100 extrasolar planetary systems. We investigate the uncertainty in the orbital solutions that have been fit to these observations. Understanding these uncertainties will…
Radar odometry is crucial for robust localization in challenging environments; however, the sparsity of reliable returns and distinctive noise characteristics impede its performance. This paper introduces geometrically-constrained…
Navigation of a team of autonomous underwater vehicles (AUVs) coordinated by an unmanned surface vehicle (USV) is efficient and reliable for deep ocean exploration. AUVs depart from and return to the USV after collaborative navigation, data…
When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families of unstable periodic orbits break up into whiskered tori, with most tori persisting into the perturbed system. In this study, we 1) develop a…
Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching…
Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localisation…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…