Axial Isometries of Manifolds of Non-Positive Curvature.
Axiom A Actions.
Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models
We consider a family of planar systems introduced in 1991 by Benedicks and Carleson as a toy model for the dynamics of the so-called Hénon maps. We show that Smale’s Axiom A property is -dense among the systems in this family, despite the existence of -open subsets (closely related to the so-called Newhouse phenomena) where Smale’s Axiom A is violated. In particular, this provides some evidence towards Smale’s conjecture that Axiom A is a -dense property among surface diffeomorphisms. The basic...
Axiomatic theory of divergent series and cohomological equations
A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some cohomological equations, all solutions to which are nonmeasurable. In particular, this realizes a construction of a nonmeasurable function as first conjectured by Kolmogorov.
Bäcklund transformations for first and second Painlevé hierarchies.
Bäcklund transformations for several cases of a type of generalized KdV equation.
Bäcklund transformations for the Kirchhoff top.
Bäcklund transformations for the trigonometric Gaudin magnet.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Backlund-Darboux Transformations in Sato's Grassmannian
We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.
Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural network
In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics....
Baker domains for Newton’s method
For an entire function let be the Newton function associated to . Each zero of is an attractive fixed point of and is contained in an invariant component of the Fatou set of the meromorphic function in which the iterates of converge to . If has an asymptotic representation , in a sector , then there exists an invariant component of the Fatou set where the iterates of tend to infinity. Such a component is called an invariant Baker domain.A question in the opposite direction...
Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards
We consider a random walk in a stationary ergodic environment in , with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right which implies that there are no “traps.” We prove the law of large numbers with positive speed, as well as the ergodicity of the environment seen from the particle. Then, we consider Knudsen stochastic billiard with a drift in a random tube in , , which serves as environment....
Banach principle in the space of τ-measurable operators
We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.
Bar Billiards and Poncelet’s Porism
Basic Brane Mechanics
Basic properties of shift radix systems.
Basics of Lagrangian foliations.
The paper is an exposition of basic known local and global results on Lagrangian foliations such as the Theorem of Darboux-Lie, Weinstein, Arnold-Liouville, a global characterization of cotangent bundles, higher order Maslov classes, etc.
Bayesian methods in hydrology: a review.
Hydrology and water resources management are inherently affected by uncertainty in many of their involved processes, including inflows, rainfall, water demand, evaporation, etc. Statistics plays, therefore, an essential role in their study. We review here some recent advances within Bayesian statistics and decision analysis which will have a profound impact in these fields.
Behavior of quasiregular semigroups near attracting fixed points.