We consider a dynamical system that exhibits transition chains of invariant tori alternating with Birkhoff zones of instability in a 2-dimensional center manifold. It is known that there exist orbits that shadow the transition chains. It is also known that there exist orbits that cross the Birkhoff zones of instability. We describe a topological mechanism that allows one to join together the tw...

A method for obtaining the correlation of atwo Hermite neural network is developed. The method is based on the fact that a Hermite function is unchanged by the Fourier transform, which allows an expression for the correlation to be obtained directly from the network weights without the need for the Fourier transform. Comparative results with other neural network correlation methods are presente...

We prove that the Birkhoff map Ω for KdV constructed on H 0 (T) can be interpolated between H 0 (T) and L20(T). In particular, the symplectic phase space H 1/2 0 (T) can be described in terms of Birkhoff coordinates.

In this note, we give an account of further development of generalized Hermite constants after [W1]. In [W5], we introduced the fundamental Hermite constant γ(G,Q, k) of a pair (G,Q) of a connected reductive group G and a maximal parabolic subgroup Q of G both defined over a global field k. Though we use adelic language, the definition of γ(G,Q, k) is given as a natural generalization of the de...

For a subshift of finite type and a fixed Hölder continuous function, the zero measure invariant set of points where the Birkhoff averages do not exist is either empty or carries full Hausdorff dimension. Similar statements hold for conformal repellers and two-dimensional horseshoes, and the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages...

In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrödinger operators. In particular we give a ”non-symbolic” operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.

In this paper, we consider two interpolations of Birkhoff-type with integer-order derivative. The Birkhoff interpolation is related with collocation method for the corresponding initial or boundary value problems of differential equations. The solvability of the interpolation problems is proved. For Gauss-type interpolating points, error of interpolation approximation is deduced. Also, we give ...

To produce grids conforming to the boundary of a physical domain with boundary orthogonality features, algebraic methods like transfinite interpolating schemes can be profitably used. Moreover, the coupling of Hermite-type (also interpolating prescribed boundary direction) schemes with elliptic methods turns out to be effective to overcome the drawback of both algebraic and elliptic strategies....