Related papers: An abstract KAM theorem
A general theory of the beam interaction with small discontinuities of the vacuum chamber is developed taking into account the reaction of radiated waves back on the discontinuity. The reactive impedance calculated earlier is reproduced as…
Commutative $d$-torsion $K$-theory is a variant of topological $K$-theory constructed from commuting unitary matrices of order dividing $d$. Such matrices appear as solutions of linear constraint systems that play a role in the study of…
A selfcontained proof of the KAM theorem in the Thirring model is discussed.
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results…
In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum…
An extended coherent state for describing a system of two interacting quanum objects is considered. A modified perturbation theory based on using the extended coherent states is formulated.
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
The paper consists of two sections. In Section 1, we give a short review of KAM theory with an emphasis on Whitney smooth families of invariant tori in typical Hamiltonian and reversible systems. In Section 2, we prove a KAM-type result for…
KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by V.I.Arnold in the 60s who worked out a theorem, that he named the Fundamental Theorem…
The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non contractive iterated…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
For an integrable Hamiltonian with $d\ (d\geq 2)$ degrees of freedom, we show the conditions on perturbations, for which invariant tori can be destructed.
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among the matters with different levels of hierarchy is appreciated. It is shown that the general…
A number of studies have shown that chaos occurs in scattering: the outgoing deflection angle is seen to be an erratic function of the impact parameter. We propose to extend this to quantum field theory, and to use erratic behavior of the…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
We prove that there is an invariant torus with given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for…
We give a proof of the KAM theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is…