Space of initial values of a map with a quartic invariant

2020/02/24 by Gubbiotti, G., Joshi, N.
#14E05 #14E15 #14H70 #14J17 #37F10 #39A10 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2002.10089

Abstract

We compactify and regularize the space of initial values of a planar map with a quartic invariant and use this construction to prove its integrability in the sense of algebraic entropy. The system turns out to have certain unusual properties, including a sequence of points of indeterminacy in \mathbb P¹\cross \mathbb P¹. These indeterminacy points are shown to lie on a singular fibre of the mapping to a corresponding QRT system and provide the existence of a one-parameter family of special solutions.

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