arXiv subjects

Jérôme Daquin

Publications and source records attributed to Jérôme Daquin.

4 recordsLinked to original sources

arXiv2026

Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane

We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynamical systems (DSs). Morphologically, they are characterized by a branch and a soma with several vertices (arms) and sometimes with multiple periodicities. A bunch of infinite astrocytes emerge through their branches from a region, in general, of low periodicity. Astrocytes are embedded in a quasiperiodic-chaotic scenario. The soma complexity (number of vertices) determines a kind of hierarchy of the astrocytes; moreover, bunches of subsequent structures from the astrocyte have been emphasized, revealing a self-similarity property. We conducted a detailed analysis in a Zeeman laser model, but we also observed astrocytes in many other DSs. The multiperiodicity exhibited by the astrocytes in their soma gives rise to harlequin dress-like patterns and tri-, quad-, and quint-critical points, which indicate the coexistence of different higher-order periodicities. In the concave borders of the soma, a doubling cascade of quint-points emerges as a bifurcation in the PP, defining regions of ordered sequences of higher periodicity in the route to chaos.

nlin.CD↗

arXiv2025

Improved detection of chaos with Lagrangian descriptors using differential algebra

Lagrangian descriptors (LDs) based on the arc length of orbits previously demonstrated their utility in delineating structures governing the dynamics. Recently, a chaos indicator based on the second derivatives of the LDs, referred to as $\vert\vert Δ\rm{LD} \vert\vert$, has been introduced to distinguish regular and chaotic trajectories. Thus far, the derivatives are numerically approximated using finite differences on fine meshes of initial conditions. In this paper, we instead use the differential algebra (DA) framework as a form of automatic differentiation to introduce and compute $\vert\vert Δ\rm{LD} \vert\vert$ up to machine precision. We discuss and exemplify benefits of this framework, such as the determination of reliable thresholds to distinguish ordered from chaotic trajectories. Our extensive parametric study quantitatively assesses the accuracy and sensitivity of both the finite differences and differential arithmetic approaches by focusing on paradigmatic discrete models of Hamiltonian chaos, namely the Chirikov's standard map and coupled $4$-dimensional variants. Our results demonstrate that finite difference techniques for $\vert\vert Δ\rm{LD} \vert\vert$ might lead to significant misclassification rate, up to $20\%$ when the phase space supports thin resonant webs, due to the difficulty to determine appropriate thresholds. On the contrary, $\vert\vert Δ\rm{LD} \vert\vert$ computed through DA arithmetic leads to clear bimodal distributions which in turn lead to robust thresholds. As a consequence, the DA framework reveals as sensitive as established first order tangent map based indicators, independently of the underlying dynamical regime. Finally, the benefits of the DA framework are also highlighted for non-uniform depleted meshes of initial conditions.

nlin.CD↗

arXiv2024

The Resident Space Objects Network: a complex system approach for shaping space sustainability

Near-Earth space continues to be the focus of critical services and capabilities provided to the society. With the steady increase of space traffic, the number of Resident Space Objects (RSOs) has recently boomed in the context of growing concern due to space debris. The need of a holistic and unified approach for addressing orbital collisions, assess the global in-orbit risk, and define sustainable practices for space traffic management has emerged as a major societal challenge. Here, we introduce and discuss a versatile framework rooted on the use of the complex network paradigm to introduce a novel risk index for space sustainability criteria. With an entirely data-driven, but flexible, formulation, we introduce the Resident Space Object Network (RSONet) by connecting RSOs that experience near-collisions events over a finite-time window. The structural collisional properties of RSOs are thus encoded into the RSONet and analysed with the tools of network science. We formulate a geometrical index highlighting the key role of specific RSOs in building up the risk of collisions with respect to the rest of the population. Practical applications based on Two-Line Elements and Conjunction Data Message databases are presented.

astro-ph.EP↗

arXiv2020

Symbolic dynamics in a binary asteroid system

We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczyński, combined with a recent analysis of an associated secular problem.

math.DS↗