Periodic Orbits of Planar Integrable Birational Maps

Gálvez-Carrillo, Imma; Mañosa, Vı́ctor

doi:10.1007/978-3-319-12328-8_2

Springer Proceedings in Mathematics &Amp; Statistics

2015

DOI: 10.1007/978-3-319-12328-8_2

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Periodic Orbits of Planar Integrable Birational Maps

Imma Gálvez-Carrillo

Vı́ctor Mañosa

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Lie symmetries of birational maps preserving genus 0 fibrations

Llorens

Mañosa

2015

Journal of Mathematical Analysis and Applications

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We prove that any planar birational integrable map, which preserves a fibration given by genus 0 curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics of these maps. Using this approach, the dynamics of several maps is described. In particular we are able to give, for particular examples, the explicit expression of the rotation number function, and the set of periods of the considered maps.

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Lie symmetries of birational maps preserving genus 0 fibrations

Llorens

Mañosa

2015

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

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Periodic Orbits of Planar Integrable Birational Maps

Cited by 1 publication

References 42 publications

Lie symmetries of birational maps preserving genus 0 fibrations

Lie symmetries of birational maps preserving genus 0 fibrations

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