Lie symmetries of birational maps preserving genus 0 fibrations
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 m...
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| Veröffentlicht in: | Journal of mathematical analysis and applications Jg. 432; H. 1; S. 531 - 549 |
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01.12.2015
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| Abstract | 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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| AbstractList | 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. 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. Peer Reviewed |
| Author | Mañosa, Víctor Llorens, Mireia |
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| Cites_doi | 10.1016/j.jmaa.2004.06.035 10.1006/jsco.1996.0084 10.1016/j.jde.2007.10.013 10.1088/0305-4470/39/5/008 10.1353/ajm.2001.0038 10.1016/S0378-4371(96)00142-2 10.1142/S0218127412502665 10.1088/1751-8113/40/42/S20 10.1142/S0218127406015027 10.1007/s12346-011-0047-8 10.1512/iumj.1996.45.1331 |
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| Keywords | Integrable maps Periodic orbits Lie symmetries Rational parameterizations |
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| References | Diller, Favre (br0070) 2001; 123 Cima, Mañosas (br0050) 2011; 10 Saito, Saitoh (br0130) 2007; 40 Bastien, Rogalski (br0010) 2004; 300 Cima, Gasull, Mañosa (br0040) 2008; 244 Jogia, Roberts, Vivaldi (br0110) 2006; 39 Sushko, Gardini (br0150) 2009; 345 Diller (br0060) 1996; 45 Sendra, Winkler, Pérez-Diaz (br0140) 2008 Haggar, Byrnes, Quispel, Capel (br0090) 1996; 233 Gálvez, Mañosa (br0080) 2015; vol. 112 Cima, Gasull, Mañosa (br0030) 2006; 16 Bastien, Rogalski (br0020) 2012; 22 van Hoeij (br0100) 1997; 23 Palladino (br0120) Diller (10.1016/j.jmaa.2015.06.069_br0060) 1996; 45 Sushko (10.1016/j.jmaa.2015.06.069_br0150) 2009; 345 Bastien (10.1016/j.jmaa.2015.06.069_br0010) 2004; 300 Cima (10.1016/j.jmaa.2015.06.069_br0030) 2006; 16 Cima (10.1016/j.jmaa.2015.06.069_br0040) 2008; 244 van Hoeij (10.1016/j.jmaa.2015.06.069_br0100) 1997; 23 Diller (10.1016/j.jmaa.2015.06.069_br0070) 2001; 123 Bastien (10.1016/j.jmaa.2015.06.069_br0020) 2012; 22 Haggar (10.1016/j.jmaa.2015.06.069_br0090) 1996; 233 Cima (10.1016/j.jmaa.2015.06.069_br0050) 2011; 10 Palladino (10.1016/j.jmaa.2015.06.069_br0120) Sendra (10.1016/j.jmaa.2015.06.069_br0140) 2008 Jogia (10.1016/j.jmaa.2015.06.069_br0110) 2006; 39 Saito (10.1016/j.jmaa.2015.06.069_br0130) 2007; 40 Gálvez (10.1016/j.jmaa.2015.06.069_br0080) 2015; vol. 112 |
| References_xml | – volume: 123 start-page: 1135 year: 2001 end-page: 1169 ident: br0070 article-title: Dynamics of bimeromorphic maps of surfaces publication-title: Amer. J. Math. – ident: br0120 article-title: On invariants and forbidden sets – volume: 39 start-page: 1133 year: 2006 end-page: 1149 ident: br0110 article-title: An algebraic geometric approach to integrable maps of the plane publication-title: J. Phys. A: Math. Gen. – volume: 23 start-page: 209 year: 1997 end-page: 227 ident: br0100 article-title: Rational parameterizations of algebraic curves using a canonical divisor publication-title: J. Symbolic Comput. – volume: 45 start-page: 721 year: 1996 end-page: 772 ident: br0060 article-title: Dynamics of birational maps of publication-title: Indiana Univ. Math. J. – volume: 345 start-page: 254 year: 2009 end-page: 279 ident: br0150 article-title: Center bifurcation of a point on the Poincaré equator publication-title: Grazer Math. Ber. – volume: vol. 112 year: 2015 ident: br0080 article-title: Periodic orbits of planar integrable birational maps publication-title: Nonlinear Maps and Their Applications – volume: 16 start-page: 631 year: 2006 end-page: 645 ident: br0030 article-title: Dynamics of rational discrete dynamical systems via first integrals publication-title: Internat. J. Bifur. Chaos – volume: 22 start-page: 1250266 year: 2012 ident: br0020 article-title: A biquadratic system of two order one difference equations: periods, chaotic behavior of the associated dynamical system publication-title: Internat. J. Bifur. Chaos – volume: 244 start-page: 630 year: 2008 end-page: 648 ident: br0040 article-title: Studying discrete dynamical systems through differential equations publication-title: J. Differential Equations – volume: 300 start-page: 303 year: 2004 end-page: 333 ident: br0010 article-title: On some algebraic difference equations publication-title: J. Math. Anal. Appl. – year: 2008 ident: br0140 article-title: Rational Algebraic Curves – volume: 233 start-page: 379 year: 1996 end-page: 394 ident: br0090 article-title: -integrals and publication-title: Phys. A – volume: 10 start-page: 247 year: 2011 end-page: 275 ident: br0050 article-title: Real dynamics of integrable birational maps publication-title: Qual. Theory Dyn. Syst. – volume: 40 start-page: 12775 year: 2007 end-page: 12787 ident: br0130 article-title: On recurrence equations associated with invariant varieties of periodic points publication-title: J. Phys. A: Math. Gen. – volume: 300 start-page: 303 year: 2004 ident: 10.1016/j.jmaa.2015.06.069_br0010 article-title: On some algebraic difference equations un+2un=ψ(un+1) in R+, related to families of conics or cubics: generalization of the Lyness' sequences publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.06.035 – volume: 23 start-page: 209 year: 1997 ident: 10.1016/j.jmaa.2015.06.069_br0100 article-title: Rational parameterizations of algebraic curves using a canonical divisor publication-title: J. Symbolic Comput. doi: 10.1006/jsco.1996.0084 – volume: vol. 112 year: 2015 ident: 10.1016/j.jmaa.2015.06.069_br0080 article-title: Periodic orbits of planar integrable birational maps – volume: 244 start-page: 630 year: 2008 ident: 10.1016/j.jmaa.2015.06.069_br0040 article-title: Studying discrete dynamical systems through differential equations publication-title: J. Differential Equations doi: 10.1016/j.jde.2007.10.013 – ident: 10.1016/j.jmaa.2015.06.069_br0120 – volume: 39 start-page: 1133 year: 2006 ident: 10.1016/j.jmaa.2015.06.069_br0110 article-title: An algebraic geometric approach to integrable maps of the plane publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/39/5/008 – year: 2008 ident: 10.1016/j.jmaa.2015.06.069_br0140 – volume: 123 start-page: 1135 year: 2001 ident: 10.1016/j.jmaa.2015.06.069_br0070 article-title: Dynamics of bimeromorphic maps of surfaces publication-title: Amer. J. Math. doi: 10.1353/ajm.2001.0038 – volume: 233 start-page: 379 year: 1996 ident: 10.1016/j.jmaa.2015.06.069_br0090 article-title: k-integrals and k-Lie symmetries in discrete dynamical systems publication-title: Phys. A doi: 10.1016/S0378-4371(96)00142-2 – volume: 22 start-page: 1250266 year: 2012 ident: 10.1016/j.jmaa.2015.06.069_br0020 article-title: A biquadratic system of two order one difference equations: periods, chaotic behavior of the associated dynamical system publication-title: Internat. J. Bifur. Chaos doi: 10.1142/S0218127412502665 – volume: 345 start-page: 254 year: 2009 ident: 10.1016/j.jmaa.2015.06.069_br0150 article-title: Center bifurcation of a point on the Poincaré equator publication-title: Grazer Math. Ber. – volume: 40 start-page: 12775 year: 2007 ident: 10.1016/j.jmaa.2015.06.069_br0130 article-title: On recurrence equations associated with invariant varieties of periodic points publication-title: J. Phys. A: Math. Gen. doi: 10.1088/1751-8113/40/42/S20 – volume: 16 start-page: 631 year: 2006 ident: 10.1016/j.jmaa.2015.06.069_br0030 article-title: Dynamics of rational discrete dynamical systems via first integrals publication-title: Internat. J. Bifur. Chaos doi: 10.1142/S0218127406015027 – volume: 10 start-page: 247 year: 2011 ident: 10.1016/j.jmaa.2015.06.069_br0050 article-title: Real dynamics of integrable birational maps publication-title: Qual. Theory Dyn. Syst. doi: 10.1007/s12346-011-0047-8 – volume: 45 start-page: 721 year: 1996 ident: 10.1016/j.jmaa.2015.06.069_br0060 article-title: Dynamics of birational maps of P2 publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1996.45.1331 |
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| Snippet | 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... |
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| SubjectTerms | 37 Dynamical systems and ergodic theory 37C Smooth dynamical systems: general theory 37E Low-dimensional dynamical systems 39 Difference and functional equations 39A Difference equations Classificació AMS Differentiable dynamical systems Equacions diferencials i integrals Foliacions (Matemàtica) Foliations (Mathematics) Integrable maps Lie symmetries Matemàtiques i estadística Periodic orbits Rational parameterizations Sistemes dinàmics diferenciables Àrees temàtiques de la UPC |
| Title | Lie symmetries of birational maps preserving genus 0 fibrations |
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