  In this paper, we develop a dynamical system counterpart to the term sparsity
sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization.
This allows for computational savings and improved scalability while preserving
convergence guarantees when sum-of-squares methods are applied to problems from
dynamical systems, including the problems of approximating region of
attraction, the maximum positively invariant set, and the global attractor. At
its core, the method exploits the algebraic structure of the data, thereby
complementing existing methods that exploit causality relations among the
states of the dynamical system. The procedure encompasses sign symmetries of
the dynamical system as was already revealed for polynomial optimization.
Numerical examples demonstrate the efficiency of the approach in the presence
of this type of sparsity.
