We compactify and regularise 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 has certain unusual properties, including a sequence of points of indeterminacy in. These indeterminacy points 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.
Space of Initial Values of a Map with A Quartic Invariant / G. Gubbiotti, N. Joshi. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - 103:3(2021), pp. 438-449. [10.1017/S0004972720000751]
Space of Initial Values of a Map with A Quartic Invariant
G. Gubbiotti;
2021
Abstract
We compactify and regularise 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 has certain unusual properties, including a sequence of points of indeterminacy in. These indeterminacy points 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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