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An experimental test of the local fluctuation theorem in chains of weakly interacting Anosov systems
Giovanni Gallavotti, Fabio Perroni
An experimental test of a large fluctuation theorem is performed on a chain of coupled ``cat maps''. Our interest is focused on the behavior of a subsystem of this chain. A local e…
Quasi periodic motions from Hipparchus to Kolmogorov
Giovanni Gallavotti
The evolution of the conception of motion as composed by circular uniform motions is analyzed, stressing its continuity from antiquity to our days.
Ergodic and chaotic hypotheses: nonequilibrium ensembles in statistical mechanics and turbulence
Giovanni Gallavotti
The ergodic hypothesis outgrew from the ancient conception of motion as periodic or quasi periodic. It did cause a revision of our views of motion, particularly through Boltzmann a…
A local fluctuation theorem
Giovanni Gallavotti
A mechanism for the validity of a local version of the fluctuation theorem, uniform in the system size, is discussed for a reversible chain of weakly coupled Anosov systems.
Chaotic Hypothesis and Universal Large Deviations Properties
Giovanni Gallavotti
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be…
Reminiscences on science at I.H.E.S. A problem on homoclinic theory and a brief review
Giovanni Gallavotti
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…
Melnikov's approximation dominance. Some examples
G. Gallavotti, G. Gentile, V. Mastropietro
We continue a previous paper to show that Mel'nikov's first order formula for part of the separatrix splitting of a pendulum under fast quasi periodic forcing holds, in special exa…
Homoclinic splitting, II. A possible counterexample to a claim by Rudnev and Wiggins on Physica D
G. Gallavotti, G. Gentile, V. Mastropietro
Results in the mentioned paper do not seem valid.
Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scales systems
Giovanni Gallavotti, Guido Gentile, Vieri Mastropietro
Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different cha…
Chaotic dynamics, fluctuations, nonequilibrium ensembles
Giovanni Gallavotti
A review of some recent results and ideas about the expected behaviour of large chaotic systems and fluids.
Hamilton--Jacobi's equation and Arnold's diffusion near invariant tori in a priori unstable isochronous systems
Giovanni Gallavotti
Local integrability of hyperbolic oscillators is discussed to provide an introductory example of the Arnold's diffusion phenomenon in a forced pendulum. This is a text prepared for…
Fast Arnold's diffusion in isochronous systems
Giovanni Gallavotti
We provide an illustration of a mechanism for Arnold's diffusion following a nonvariational approach and find explicit estimates for the diffusion time.
Pendulum: separatrix splitting
G. Gallavotti, G. Gentile, V. Mastropietro
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann…
Fluctuation patterns and conditional reversibility in nonequilibrium systems
G. Gallavotti
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibri…
SRB states and nonequilibrium statistical mechanics close to equilibrium
Giovannni Gallavotti, David Ruelle
Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula for their derivatives with respect to parameters. We write general expressions f…
New methods in nonequilibrium gases and fluids
Giovannni Gallavotti
Kinematical and dynamical properties of chaotic systems are reviewed and a few applications are described.
Quasi linear flows on tori: regularity of their linearization
Federico Bonetto, Giovanni Gallavotti, Guido Gentile +1
Under suitable conditions a flow on a torus --close, with large enough, to a quasi periodic diophantine rotation is shown to be conjugated to the quasi periodic rotati…
Dynamical ensembles equivalence in fluid mechanics
Giovanni Gallavotti
Dissipative Euler and Navier Stokes equations are discussed with the aim of proposing several experiments apt to test the equivalence of dynamical ensembles and the chaotic hypothe…
Chaotic principle: an experimental test
F. Bonetto, G. Gallavotti, P. L. Garrido
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validi…
Equivalence of dynamical ensembles and Navier Stokes equations
Giovanni Gallavotti
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. Th…
Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
Giovanni Gallavotti
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…
Lindstedt series, ultraviolet divergences and Moser's theorem
F. Bonetto, G. Gallavotti, G. Gentile +1
Moser's invariant tori for a class of nonanalytic quasi integrable even hamiltonian systems are shown to be analytic in the perturbation parameter. We do so by exhibiting a summati…
A rigorous implementation of the Jeans--Landau--Teller approximation
G. Benettin, A. Carati, G. Gallavotti
Rigorous bounds on the rate of energy exchanges between vibrational and translational degrees of freedom are established in simple classical models of diatomic molecules. The resul…
Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
Giovanni Gallavotti
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 t…