Periodic orbits close to elliptic tori and applications to the three-body problem

We prove, under suitable non-resonance and non-degeneracy ``twist'' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets''. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.

Saggezza o filosofia pratica?

The so called “revival of practical philosophy”, started in 1960 by H.G. Gadamer with his Wahrheit und Methode e metodo”, has often provoked a confusion between the authentic prac-tical philosophy of Aristotle and the virtue he calls phronêsis or wisdom. Actually, they repre-sent two forms of knowledge very different. Wisdom is the virtue of practical reason which consists in the ability of correctly deliberate, that is in the ability of individuating the action more suitable for realizing a good end. On the contrary, practical philosophy is a science, that is an habit of theoretical reason, even if it is a practical science, which has as its end in the good action and has a degree of rigour inferior to that of theoretical sciences. Practical philosophy is the science of the supreme good for man, that is happiness – the full flourishing of all human capabilities-, which is determined by means of a dialectical discussion with the thesis of the various philosophers

Philosophy and Human Rights

It is common knowledge that modern political societies, and to even greater extent contemporary ones, are characterized by pluralism. The term is used to describe situations which contain within the same society individuals and groups associated by various religions, various cultures, and various ethical systems. This is the consequence of several historical phenomena of widespread influence, which began in modern epoch and has intensified in the contemporary era, such as secularization, emigration, the establishment of democratic regimes in an even-larger number of states. The thesis defended here is that the function of what Aristotle called the endoxa today can be performed by human rights, that is by the statements contained in the great declarations of rights found in national constitutional documents and in charters of the great international organizations, such as the United Nations, the Council of Europe, the Organization of African Unity, the Organization of the Islamic Conference, etc.Es sabido que las sociedades políticas modernas, así como a las contemporáneas aún en mayor medida, se caracterizan por el pluralismo. El término se utiliza para describir situaciones que contienen dentro de los individuos de una misma sociedad y grupos asociados de diversas religiones, culturas diferentes y diversos sistemas éticos. Esta es la consecuencia de varios fenómenos históricos de gran influencia, que se iniciaron en la época moderna y se ha intensificado en la era contemporánea, como la secularización, la emigración, el establecimiento de regímenes democráticos en un número aún mayor de-estados. La tesis defendida aquí es que la función de lo que Aristóteles llamaba la endoxa hoy puede ser llevada cabo por los derechos humanos, es decir por las declaraciones contenidas en las grandes declaraciones de derechos contenidas en los documentos de constitución y en los estatutos de las grandes organizaciones internacionales, como la de las Naciones Unidas, el Consejo de Europa, la Organización de la Unidad Africana, la Organización de la Conferencia Islámica, etc

Il carattere dialettico del cogito

Il famoso método cartesiano è senza dubbio un método intuitivo-deduttivo, cioè consiste nel partiré da intuizioni assolutamente certe, le quali fungono da principi, e nel dedurne le conseguenze che necessariamente ne derivano. Esso è infatti ¡I método delia matemático, più precisamente delia geometria.1 Invece il modo seguito da Descartes per stabilire i principi, almeno perquanto riguarda il Cogito, è completamente diverso e può essere definito dialettico, se con questo termine si intende non I'arte scolastica della disputa, come pensava lo stesso Descartes, bensl la dimostrazione per confutazione, praticata da Socrate, da Platone e da Aristotele nella difesa del principio di non-contraddizione

Metafísica y libertad en la filosofía antigua

In Greek philosophy there are two rival accounts of the relation between ontology and freedom. In one of them the universe has its origin in the act of free will of an intelligence. This entails, of course, that this intelligence must be free. In the other the universe comes from necessity from an impersonal being which has not the features of an intelligent being and cannot be free

Particle-laden two-dimensional elastic turbulence

The aggregation properties of heavy inertial particles in the elastic turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are investigated by means of extensive numerical simulations in two dimensions. Both the small and large scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the properties of the advecting viscoelastic flow. We find that particles preferentially accumulate on thin highly elastic propagating waves and that this effect is largest for intermediate values of particle inertia. We provide a quantitative characterization of this phenomenon that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of correlation dimension close to 1. At larger scales, particles are found to undergo turbophoretic-like segregation. Indeed, our results indicate a close relationship between the profiles of particle density and fluid velocity fluctuations. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing.Comment: 12 pages, 9 figures. Submitted to EPJ

Natura e generazione degli animali in aristotele

riASSUnto Quest'articolo discute introduce il senso della physis concepita come generazione per introdurre la discussione di un difficile passo Della Generazione degli Animali (De gen. an. II 3, 736b21-29) sull'origine dell'intelletto. In seguito ad una minuziosa analisi di diversi testi di distinte opere di Aristotele su quest'aporia, l'autore conclude, contrariamente a l'interpretazione tradizionale, che l'intelletto non viene dal di fuori (thyrathen) ma si origina dallo pneuma contenuto nello sperma stesso. Questo pneuma essendo analogo all'etere e in certo modo divino, giustificando cosi la divinita dell'intelletto anche se non giustifica la sua provenienza dal esterno, come in genere sostengono gli interpreti