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Search Results: 1 - 10 of 5569 matches for " Giovanni Gallavotti "
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Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review
Giovanni Gallavotti
Physics , 1993, DOI: 10.1142/S0129055X9400016X
Abstract: Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the rotators are decoupled and we study the invariant tori of the rotators system at fixed rotation numbers: we exhibit cancellations, to all orders of perturbation theory, that allow proving the stability and analyticity of the dipohantine tori. We find in this way a proof of the KAM theorem by direct bounds of the $k$--th order coefficient of the perturbation expansion of the parametric equations of the tori in terms of their average anomalies: this extends Siegel's approach, from the linearization of analytic maps to the KAM theory; the convergence radius does not depend, in this case, on the twist strength, which could even vanish ({\it "twistless KAM tori"}). The same ideas apply to the case in which the potential couples the pendulum and the rotators: in this case the invariant tori with diophantine rotation numbers are unstable and have stable and unstable manifolds ({\it "whiskers"}): instead of studying the perturbation theory of the invariant tori we look for the cancellations that must be present because the homoclinic intersections of the whiskers are {\it "quasi flat"}, if the rotation velocity of the quasi periodic motion on the tori is large. We rederive in this way the result that, under suitable conditions, the homoclinic splitting is smaller than any power in the period of the forcing and find the exact asymptotics in the two dimensional cases ({\it e.g.} in the case of a periodically forced pendulum). The technique can be applied to study other quantities: we mention, as another example, the {\it homoclinic scattering phase shifts}.}
Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
Giovanni Gallavotti
Physics , 1996, DOI: 10.1103/PhysRevLett.77.4334
Abstract: The fluctuation theorem (FT), the first derived consequence of the {\it Chaotic Hypothesis} (CH) of ref. [GC1], can be considered as an extension to arbitrary forcing fields of the fluctuation dissipation theorem (FD) and the corresponding Onsager reciprocity (OR), in a class of reversible nonequilibrium statistical mechanical systems.
Reminiscences on science at I.H.E.S. A problem on homoclinic theory and a brief review
Giovanni Gallavotti
Physics , 1998,
Abstract: On the occasion of the 40-th anniversary of IHES I present a few scientific reminiscences: most of my scientific life has been marked by my visits and I run through them concluding with the analysis of a problem that originated during my last visit. The problem is to develop a convergent perturbative algorithm for the construction of the ``Eliasson's potential'' for the stable and unstable manifolds of an invariant torus: and to study its properties. A brief review follows.
Fast Arnold's diffusion in isochronous systems
Giovanni Gallavotti
Physics , 1997,
Abstract: We provide an illustration of a mechanism for Arnold's diffusion following a nonvariational approach and find explicit estimates for the diffusion time.
Quantum Nonequilibrium and Entropy creation
Giovanni Gallavotti
Physics , 2007,
Abstract: In sharp contrast to the corresponding classical systems cases it is not yet understood how to define a mechanical quantity with the interpretation of entropy creation rate for nonequilibrum stationary states of finite quantum systems with finite thermostats. Some aspects of this problem are discussed here in cases in which identifying entropy creation rate as a mechanical observable might be possible. v.2: last paragraph of Sec.2 corrected
Reversible Anosov diffeomorphisms and large deviations
Giovanni Gallavotti
Physics , 1995,
Abstract: The volume contraction obeys a large deviation rule.
Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
Giovanni Gallavotti
Physics , 1995, DOI: 10.1007/BF02174123
Abstract: It is shown that the "chaoticity hypothesis", analogous to Ruelle's principle for turbulence and recently introduced in statistical mechanics, implies the Onsager reciprocity and the fluctuation dissipation theorem in various models for coexisting transport phenomena.
Thermostats, chaos and Onsager reciprocity
Giovanni Gallavotti
Physics , 2008, DOI: 10.1007/s10955-008-9655-3
Abstract: Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the phase space contraction rate and the currents have been linked to its derivatives with respect to the parameters measuring the forcing intensities. In some instances Green-Kubo formulae, hence Onsager reciprocity, have been related to the fluctuation theorem. However, mainly when dissipation takes place at the boundary (as in gases or liquids in contact with thermostats), phase space contraction may be independent on some of the forcing parameters or, even in absence of forcing, phase space contraction may not vanish: then the relation with the fluctuation theorem does not seem to apply. On the other hand phase space contraction can be altered by changing the metric on phase space: here this ambiguity is discussed and employed to show that the relation between the fluctuation theorem and Green-Kubo formulae can be extended and is, by far, more general.
Chaotic principle: some applications to developed turbulence
Giovanni Gallavotti
Physics , 1995, DOI: 10.1007/BF02183608
Abstract: Some models for developed turbulence are considered; they are shown to obey a large fluctuations theorem, and one among them also obeys a response reciprocity relation of Onsager's type. This illustrates and extends ideas and techniques developed in earlier works mainly for non equilibrium problems in statistical mechanics.
Equivalence of dynamical ensembles and Navier Stokes equations
Giovanni Gallavotti
Physics , 1996, DOI: 10.1016/S0375-9601(96)00729-3
Abstract: A reversible version of the Navier Stokes equation is studied. A conjecture emerges stating the equivalence between the reversible equation and the usual Navier Stokes equation. The latter appears as a statement of ensembles equivalence in the limit of infinite Reynolds number, which plays the role of the thermodynamic limit.
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