Computing Semi-algebraic Invariants for Polynomial Dynamical Systems

Details Computing Semi-algebraic Invariants for Polynomial Dynamical Systems Computing Semi-algebraic Invariants for Polynomial Dynamical Systems

2011-02-03

arxiv.org/abs/1102.0705v2

Computer Science

Symbolic Computation

28 pages

Scientific paper

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 and 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.

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