Invariant varieties of periodic points for some higher dimensional integrable maps

Abstract

By studying various rational integrable maps on ${\hat{\mathbf{C}}}^d$ with $p$ invariants, we show that periodic points form an invariant variety of dimension $\ge p$ for each period, in contrast to the case of nonintegrable maps in which they are isolated. We prove the theorem: {\it `If there is an invariant variety of periodic points of some period, there is no set of isolated periodic points of other period in the map.'}

24 pages

References in corpus (1)

• Spectral statistics of a quantum interval-exchange map

Cited by in corpus (5)

• On recurrence equations associated with invariant varieties of periodic points
• Derivation of Invariant Varieties of Periodic Points from Singularity Confinement in the case of Toda Map
• Singularity Confinement and Projective Resolution of Triangulated Category
• Degeneration of the Julia set to singular loci of algebraic curves
• Derivation of Higher Dimensional Periodic Recurrence Equations by Nested Structure of Complex Numbers