Motivated by the study of the Kahan–Hirota–Kimura discretisation of the Euler top, we characterise the growth and integrability properties of a collection of elements in the Cremona group of a complex projective 3-space using techniques from algebraic geometry. This collection consists of maps obtained by composing the standard Cremona transformation with projectivities that permute the fixed points of and the points over which performs a divisorial contraction. Specifically, we show that three behaviour are possible: (A) integrable with quadratic degree growth and two invariants, (B) periodic with two-periodic degree sequences and more than two invariants, and (C) non-integrable with submaximal degree growth and one invariant

Growth and Integrability of Some Birational Maps in Dimension Three / M. Graffeo, G. Gubbiotti. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - (2023), pp. 1-61. [Epub ahead of print] [10.1007/s00023-023-01339-5]

Growth and Integrability of Some Birational Maps in Dimension Three

G. Gubbiotti
2023

Abstract

Motivated by the study of the Kahan–Hirota–Kimura discretisation of the Euler top, we characterise the growth and integrability properties of a collection of elements in the Cremona group of a complex projective 3-space using techniques from algebraic geometry. This collection consists of maps obtained by composing the standard Cremona transformation with projectivities that permute the fixed points of and the points over which performs a divisorial contraction. Specifically, we show that three behaviour are possible: (A) integrable with quadratic degree growth and two invariants, (B) periodic with two-periodic degree sequences and more than two invariants, and (C) non-integrable with submaximal degree growth and one invariant
Settore MAT/07 - Fisica Matematica
2023
13-lug-2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1025230
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