Polynomial level-set method for attractor estimation

In this study, we present a polynomial level-set method for attractor estimation. This method uses the sub-level representation of sets. The problem of flowing these sets under the advection map of a dynamic system is converted to a semi-definite program, which is used to compute the coefficients of the polynomials. The required storage space for describing the result is much less than the mesh-based methods. The characteristics of attractors are used in the algorithm formulations so that the associated numerical error can be reduced. We further address the related problems of constraining the degree of the polynomials. Various numerical examples are used to show the effectiveness of the advection approach.