Algebraic dynamics solution and algebraic dynamics algorithm of Burgers equations

An algebraic solution of driven single band tight binding dynamics

The dynamics of the driven single band tight binding model for Wannier-Stark systems is formulated and solved using a dynamical algebra. This Lie algebraic approach is very convenient for evaluating matrix elements and expectation values. A classicalization of the tight binding model is discussed as well as some illustrating examples of Bloch oscillations and dynamical localization effects. It ...

Algebraic Dynamics and Transcendental Numbers

A first example of a connection between transcendental numbers and complex dynamics is the following. Let p and q be polynomials with complex coefficients of the same degree. A classical result of Böttcher states that p and q are locally conjugates in a neighborhood of∞: there exists a function f , conformal in a neighborhood of infinity, such that f(p(z)) = q(f(z)). Under suitable assumptions,...

Calabi theorem and algebraic dynamics

The aim of this paper is to prove a Calabi theorem for metrized line bundles over non-archimedean analytic spaces, and apply it to endomorphisms with the same polarization and the same set of preperiodic points over a complex projective variety. The proof uses Arakelov theory on Berkovich’s non-archimedean analytic spaces even though the results on dynamical systems can be purely stated over co...

ALGEBRAIC NONLINEARITY IN VOLTERRA-HAMMERSTEIN EQUATIONS

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

Solution of Systems of Linear Algebraic Equations