New Symbolic Procedures in the Study of Dynamical Systems

Abstract

The thesis develops symbolic representations of dynamical systems in finite-dimensional commutative real algebras. The algebraic framework (orthogonal idempotents, zero divisors, and the structure of finite-order algebras) supports algebra-valued Fourier and Laplace transforms and Walsh-function-based system identification. The methods yield exact, coordinate-free vectorial solutions for motion in non-inertial reference frames, including a generalized Larmor theorem, the Foucault pendulum, motion in central positional-force fields, and the two-body problem in arbitrarily rotating reference frames. This English edition is an audited LaTeX reconstruction of the 1995 original, with an editorial note documenting provenance.

arXiv comment104 pages. English translation of the author's 1995 doctoral thesis ("Noi procedee simbolice in studiul sistemelor dinamice", "Gheorghe Asachi" Technical University of Iasi, Romania), presented as an audited, historically conforming LaTeX reconstruction; an editorial note documents the provenance and the precise limits of the 2026 intervention