Non-integrability of measure preserving maps via Lie symmetries

Anna Cima, Armengol Gasull, Víctor Mañosa

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4 Citations (Scopus)


© 2015 Elsevier Inc. We consider the problem of characterizing, for certain natural number m, the local Cm-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability with the existence of some Lie Symmetries associated to the maps, together with the study of the finiteness of its periodic points. One of the steps in the proof uses the regularity of the period function on the whole period annulus for non-degenerate centers, question that we believe that is interesting by itself. The obtained criterion can be applied to prove the local non-integrability of the Cohen map and of several rational maps coming from second order difference equations.
Original languageEnglish
Pages (from-to)5115-5136
JournalJournal of Differential Equations
Issue number10
Publication statusPublished - 15 Nov 2015


  • Cohen map
  • Integrability and non-integrability of maps
  • Integrable vector fields
  • Lie symmetries
  • Measure preserving maps
  • Period function


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