An algebraically stable variety for a four-dimensional dynamical system reduced from the lattice super-KdV equation

2019/08/31 by A. S. Cârstea, Carstea, Adrian Stefan, Tomoyuki Takenawa +1 · 1 citation
Mathematics · Physics and Astronomy · #14E07 #37F10 #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1909.00138

openalex publication_date 2019/08/31 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

In a prior paper the authors obtained a four-dimensional discrete integrable dynamical system by the traveling wave reduction from the lattice super-KdV equation in a case of finitely generated Grassmann algebra. The system is a coupling of a Quispel-Roberts-Thompson map and a linear map but does not satisfy the singularity confinement criterion. It was conjectured that the dynamical degree of this system grows quadratically. In this paper, constructing a rational variety where the system is lifted to an algebraically stable map and using the action of the map on the Picard lattice, we prove this conjecture. We also show that invariants can be found through the same technique.

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