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Polynomial level-set methods for nonlinear dynamical systems analysis
dynamical systems analysis level-set methods
2015/6/19
In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. Th...
A nilpotent IP polynomial multiple recurrence theorem
ergodic Ramsey theory IP-sets nilpotent Hales-Jewett theorem nilpotent Szemeredi theorem
2012/6/14
We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibm...
Symmetries of Julia sets of polynomial skew products on C^2
Complex dynamics skew product Green function
2012/4/18
We consider the symmetries of Julia sets of polynomial skew products on C^2, which are birationally conjugate to rotational products. Our main results give the classification of the polynomial skew pr...
Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^2
Postcritical sets saddle basic sets Axiom A polynomial skew products C^2
2012/2/29
Investigating the link between postcritical behaviors and the relations of saddle basic sets for Axiom A polynomial skew products on C^2, we characterize various properties concerning the three kinds ...
The classification of polynomial basins of infinity
polynomial basins of infinity Dynamical Systems Complex Variables
2011/8/26
Abstract: We consider the problem of classifying the dynamics of complex polynomials $f: \mathbb{C} \to \mathbb{C}$ restricted to their basins of infinity. We synthesize existing combinatorial tools -...
Polytopic Invariant Verification and Synthesis for Polynomial Dynamical Systems via Linear Programming
Polytopic Invariant Verification Synthesis for Polynomial Dynamical Systems Linear Programming
2011/1/18
This paper deals with the veri cation and the synthesis of polytopic invariant sets for
polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state
space such that ...