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SPACE OF INITIAL VALUES OF A MAP WITH A QUARTIC INVARIANT
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 103 / Issue 3 / June 2021
- Published online by Cambridge University Press:
- 05 October 2020, pp. 438-449
- Print publication:
- June 2021
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- Article
- Export citation
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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
$\mathbb {P}^{1}\!\times \mathbb {P}^{1}$
. 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.
