Computing Semi-algebraic Invariants for Polynomial Dynamical Systems [article]

Jiang Liu and Naijun Zhan and Hengjun Zhao
2011 arXiv   pre-print
In this paper, we consider an extended concept of invariant for polynomial dynamical system (PDS) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic invariants (SAI) for such PDSs. The main idea is encoding relevant dynamical properties as conditions on the high order Lie derivatives of polynomials occurring in the SAI. A direct consequence of this criterion is a relatively complete method of SAI generation based on template assumption
more » ... semi-algebraic constraint solving. Relative completeness means if there is an SAI in the form of a predefined template, then our method can indeed find one using this template.
arXiv:1102.0705v2 fatcat:kqhsupeanngtfjaiyno5a6khgy