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X-WR-CALDESC:Events for Namur Institute For Complex Systems
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DTSTART;TZID=Europe/Brussels:20250401T130000
DTEND;TZID=Europe/Brussels:20250401T140000
DTSTAMP:20260419T134914
CREATED:20250327T113857Z
LAST-MODIFIED:20250327T113931Z
UID:2372-1743512400-1743516000@www.naxys.be
SUMMARY:Gabriele Gionti (Vatican Observatory)
DESCRIPTION:Title : ON THE CANONICAL EQUIVALENCE OF JORDAN AND EINSTEIN FRAMES \nAbstract : \nFollowing a seminal paper by Dicke\, physics should be invariant under redefinition of units of measurement\, which implies invariance under conformal transformation of the metric coefficients. This implies the longstanding issue of the equivalence between the Jordan and the Einstein frames. It is believed\, but not completely proved\, that the cosmological physical observables are the same in the two frames. Our aim is to tackle this problem from the perspective of the Hamiltonian formalism. For this reason\, we will perform the Hamiltonian analysis of the Brans-Dicke theory with Gibbons-Hawking-York boundary term both in the Jordan and the Einstein frames. The Hamiltonian Dirac’s constraint analysis will be carefully carried out in both cases and\, contrary to several claims made in the literature in the past\, it will be shown that the transformations from the Jordan to the Einstein frames do not strictly appear Hamiltonian canonical transformations on the extended phase space. We will show that if we perform a gauge fixing on the lapse and shift functions and implement them as secondary Dirac’s constraints in the ADM formalism\, the primary first-class constraints become second class. Replacing Poisson Brackets with Dirac’s Brackets and solve “strongly” the second-class constraints\, the transformation from the Jordan to the Einstein frames is Hamiltonian canonical transformation. We will briefly mention the study of the ADM formalism in the case of spherical symmetry both in the Jordan and the Einstein frames with appropriate boundary terms. We derive the equations of motion in both frames. Weintroduce the Fisher–Janis–Newman–Winicour naked singularity solution in the Einstein frame and Bocharova–Bronnikov-Melnikov-Bekenstein black hole solution in the Jordan frame. They are\, respectively\, solution of the equations of motion in the two frames and are connected by the Hamiltonian canonical transformation from the Jordan to the Einstein frames on the reduced phase space. This very fact highlights that the transformation from the Jordan to the Einstein frames is useful to generate solutions of the equations of motion in gravity. \n\n\n\n  \n\n\n\nThe seminar will take place in Room S08 at the Faculty of Sciences.
URL:https://www.naxys.be/event/gabriele-gionti-vatican-observatory/
CATEGORIES:NAXYS Seminar
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DTSTART;TZID=Europe/Brussels:20250415T130000
DTEND;TZID=Europe/Brussels:20250415T140000
DTSTAMP:20260419T134914
CREATED:20250308T105720Z
LAST-MODIFIED:20250407T090612Z
UID:2334-1744722000-1744725600@www.naxys.be
SUMMARY:Kovács Tamás (Eötvös Loránd University)
DESCRIPTION:Title : Spin-orbit dynamics under parameter drift \nAbstract : \n\n\nThe dynamics of an oblate satellite in a fixed elliptical orbit\, with its spin axis perpendicular to the orbital plane around a spherical planet\, exhibit rich coupling between rotation and orbital motion\, known as spin-orbit resonance. It is well known that the phase space of low-dimensional deterministic Hamiltonian systems contains regions of both chaotic and regular motion—namely\, chaotic bands and invariant curves (KAM tori)—depending on the initial conditions and system parameters. In the steady-state case\, these structures remain stationary. However\, when system parameters change over time\, due to various internal or external influences\, the geometry of phase space evolves accordingly. This necessitates a shift from traditional single-trajectory analysis to an ensemble-based approach\, enabling a consistent framework to describe phase space structures in non-autonomous Hamiltonian systems. In this context\, we also generalize the classical Lyapunov exponent to account for explicit time dependence\, providing a numerical stability measure for the evolving dynamics. Finally\, we propose a preliminary analytical description of the time-dependent phase space structures and their evolution.\n\n\n\n\n\n  \n\n\n\nThe seminar will take place in Room S08 at the Faculty of Sciences.
URL:https://www.naxys.be/event/kovacs-tamas-eotvos-lorand-university/
CATEGORIES:NAXYS Seminar
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BEGIN:VEVENT
DTSTART;TZID=Europe/Brussels:20250417T130000
DTEND;TZID=Europe/Brussels:20250417T140000
DTSTAMP:20260419T134914
CREATED:20250206T140153Z
LAST-MODIFIED:20250414T060340Z
UID:2311-1744894800-1744898400@www.naxys.be
SUMMARY:Judicaël Mohet (UNamur)
DESCRIPTION:Title : How to estimate the state of a nonlinear system in a linear way?  \nAbstract : \n\n\n\nIn this work\, we present a novel approach for the observer design of nonlinear systems based on a Koopman operator framework. The (linear) dual Koopman system\, associated with a nonlinear dynamic\, is introduced and analyzed in an infinite dimensional context. Moreover\, new concepts of observability and detectability are defined in the dual Koopman system\, which are shown to be equivalent to the observability and detectability of the nonlinear system\, respectively. The theoretical framework is applied to a class of holomorphic dynamics. For this class\, a Luenberger-type observer is designed for the dual Koopman system via a spectral method\, yielding an estimate of the state of the nonlinear system. Spectral observability and detectability conditions are derived in this setting\, and the exponential convergence of the Koopman observer is shown  \n\n\n\n\n\n\nAuthors: Judicaël Mohet\, Alexandre Mauroy and Joseph Winkin \n\n\n\nThe seminar will take place in Room S08 at the Faculty of Sciences.
URL:https://www.naxys.be/event/judicael-mohet-unamur/
CATEGORIES:NAXYS Seminar
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