227 research outputs found
The elements of Mechanics
No full textII edition (electronic resource): First edition (printed)
1983 Springer-Verlag,
I Edition: ISBN 0-387-11753-9, ISBN 3-540-11753-9
Since 2007 Copyright by Giovanni Gallavotti
Free download at
http://ipparco.roma1.infn.it
On homoclinic splitting problems
No full textCounterexample to a paper published earlier on Physica D by other Author
Renormalization-group approach to the theory of the Fermi surface
No full textWe describe an approach to the theory of the Fermi surface based on the renormalization group. A notion of quasi particle appears naturally in the theory. The beta function is finite to all orders of perturbation theory and we compute and discuss it to second order.
The normality of the Fermi surface is linked to the repulsivity of the quasi particle potential: the remarkable cancellations that occur in the beta function lead to think that a normal Fermi surface can perhaps occur, but only when the interaction between the quasi particles is repulsive. The approach was first proposed in an earlier paper, [BG1], and we give here an improved version of it, referring to [BG1] only to make use of technical estimates derived there
Renormalization group
No full textThe notion of renormalization group is not well
defined. It arises in theories in which a prominent role is
played by scale invariance or covariance properties,
of various quantities, with respect to a noninvertible transformation
of coordinates. The noninvertibility is an essential feature; it is
supposed to allow one to reduce effectively the difficulty of the problem.
The Book illustrates important examples of the method
Lindstedt series and Hamilton-Jacobi equation for hyperbolic tori in three time scales problems
No full text. Interacting systems consisting of two rotators and a pendulum are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of unstable quasi periodic motions in phase space is studied via Lindstedt series. The result is a strong improvement, compared to our previous results, on the domain of validity of bounds that imply existence of invariant tori, large homoclinic angles, long heteroclinic chains and drift--diffusion in phase space. x1. The Hamiltonian system. 1.1. Let ('; ff 1 ; ff 2 ) = ('; ff) 2 T 3 be three angles (i.e. positions on circles); let (I; A 1 ; A 2 ) = (I; A) 2 R 3 be their conjugate momenta (or "actions"). We consider the Hamiltonian function, depending on two parameters "; j ? 0, defined by H = j 1 2\Omega 1 A 1 + j A 2 1 2J + j \Gamma 1 2\Omega 2 A 2 + I 2 2J 0 + J 0 g 2 0 (cos ' \Gamma 1) + "f ('; ff 1 ; ff 2 ) ; (1:1) with f an even trigonometric polynomial of degree N;N 0 in ff; ..
Perturbation theory of the Fermi surface in a quantum liquid. A general quasiparticle formalism and one-dimensional systems.
No full textWe develop a perturbation theory formalism for the theory of the Fermi surface in a Fermi liquid of particles interacting via a bounded short range repulsive pair potential. The formalism is based on the renormalization group and provides a formal expansion of the large distance Schwinger functions in terms of a family of running couplings consisting of a one and two body quasi particle potentials. The flow of the running couplings is described in terms of a beta function, which is studied to all orders of perturbation theory and shown to obey, in the n–th order, n! bounds.......
Melʹnikov's approximation dominance. Some examples
No full textWe 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 examples, as an asymptotic formula in the forcing rapidity
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