1,720,972 research outputs found
How gold is the golden ratio?
No full textWe discuss the well-known importance of the golden ratio in Science and Art with few examples: its theoretical value is often taken as a good model in many applications. How good is this model in practice? We agree with many authors that more precision is needed giving, when possible, a measure of the best possible approximation. We deal with several definitions and representations, also comparing this irrational number and its rational approximations to other similar constants
Breakdown of librational invariant surfaces
Full text linkA numerical investigation of the stability of invariant librational tori is presented. The method has been developed for a model describing the spin-orbit coupling in Celestial Mechanics. Periodic orbits approaching the librational torus are computed by means of Newton's method. According to Greene's criterion, their stability is strictly related to the survival of invariant tori. We consider librational tori around the main spin-orbit resonances (1:1, 3:2). Their existence provides the stability of the resonances, due to the confinement properties in the three-dimensional phase space associated to our model. The results are consistent with the actual observations of the eccentricity and of the oblateness parameter. A different behavior of the Moon and Mercury around the main resonances is evidenced, providing interesting suggestions about the different probabilities of capture in a resonance
Esperienze di matematica in mostra: momenti e ruoli di alcune realizzazioni
No full textCosa può servire per organizzare una mostra di matematica? Quante persone si pensa di intrattenere? Su quali risorse si dovrebbe poter contare? Raccontiamo alcuni esempi provenienti dalle 11 mostre scientifiche realizzate in questi anni dal gruppo www.formulas.it, di cui facciamo parte, descrivendo i diversi ruoli e momenti che la realizzazione di una mostra richiede. A cominciare dal tema scelto e dall’interazione con gli organizzatori, passando per i diversi modi di espressione e i possibili percorsi di fruizione; dalle forme di allestimento alla produzione di oggetti da toccare e comporre, fino all’interazione con gli animatori e la valutazione dell’esito e dell’impatto sui visitatori. Descriviamo inoltre, alcune sezioni di mostre progettate in occasione di diverse edizioni del Festival del- la Scienza di Genova, seguito sempre da un pubblico numeroso e molto vario, cercando di dare un’idea dei contenuti matematici che le hanno ispirate
Singularities of periodic orbits near invariant curves
No full textWe show numerically, for standard-like maps, how the singularities (in the complex parameter) of the function which conjugates the map to a rotation of rational period behave when the period goes to an irrational number. Furthermore, we propose a numerical method to extrapolate the radius of convergence of the series parametrizing the solution of periodic orbits. The results are compared with analyses performed by Pade approximants, Greene's method, root criterion and the prediction by renormalization theory. (C) 2002 Elsevier Science B.V. All rights reserved
Rigorous KAM stability statements for non-autonomous one-dimensional hamiltonian systems
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