Applications of O-Minimality to Computational Problems in Dynamical Systems Theory

Explore how o-minimality theory applies to solving computational problems in dynamical systems, focusing on the famous Skolem Problem and linear recurrence sequences. Learn about deciding whether a linear recurrence sequence (u_n)_n equals zero for some n, formulated through linear dynamical systems involving matrices, initial points, and hyperplanes. Discover methods for determining if orbits reach or avoid specific hyperplanes, and examine advanced results on semi-algebraic sets where you can decide the existence of epsilon neighborhoods ensuring orbit avoidance. Gain insights into verification techniques for linear dynamical systems through o-minimality of real numbers, with theoretical foundations and practical computational approaches to these challenging mathematical problems.