Zoll magnetic systems on the two-torus: A Nash–Moser construction
We construct an infinite-dimensional family of smooth integrable magnetic systems on the two-torus which are Zoll, meaning that all the unit-speed magnetic geodesics are periodic. The metric and the magnetic field of such systems are arbitrarily close to the flat metric and to a given constant magne...
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| Vydáno v: | Advances in mathematics (New York. 1965) Ročník 452; s. 109826 |
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01.08.2024
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| Abstract | We construct an infinite-dimensional family of smooth integrable magnetic systems on the two-torus which are Zoll, meaning that all the unit-speed magnetic geodesics are periodic. The metric and the magnetic field of such systems are arbitrarily close to the flat metric and to a given constant magnetic field. This extends to the magnetic setting a famous result by Guillemin [19] on the two-sphere. We characterize Zoll magnetic systems as zeros of a suitable action functional S, and then look for its zeros by means of a Nash–Moser implicit function theorem. This requires showing the right-invertibility of the linearized operator dS in a neighborhood of the flat metric and constant magnetic field, and establishing tame estimates for the right inverse. As key step we prove the invertibility of the normal operator dS∘dS⁎ which, unlike in Guillemin's case, is pseudo-differential only at the highest order. We overcome this difficulty noting that, by the asymptotic properties of Bessel functions, the lower order expansion of dS∘dS⁎ is a sum of Fourier integral operators. We then use a resolvent identity decomposition which reduces the problem to the invertibility of dS∘dS⁎ restricted to the subspace of functions corresponding to high Fourier modes. The inversion of such a restricted operator is finally achieved by making the crucial observation that lower order Fourier integral operators satisfy asymmetric tame estimates. |
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| AbstractList | We construct an infinite-dimensional family of smooth integrable magnetic systems on the two-torus which are Zoll, meaning that all the unit-speed magnetic geodesics are periodic. The metric and the magnetic field of such systems are arbitrarily close to the flat metric and to a given constant magnetic field. This extends to the magnetic setting a famous result by Guillemin [19] on the two-sphere. We characterize Zoll magnetic systems as zeros of a suitable action functional S, and then look for its zeros by means of a Nash–Moser implicit function theorem. This requires showing the right-invertibility of the linearized operator dS in a neighborhood of the flat metric and constant magnetic field, and establishing tame estimates for the right inverse. As key step we prove the invertibility of the normal operator dS∘dS⁎ which, unlike in Guillemin's case, is pseudo-differential only at the highest order. We overcome this difficulty noting that, by the asymptotic properties of Bessel functions, the lower order expansion of dS∘dS⁎ is a sum of Fourier integral operators. We then use a resolvent identity decomposition which reduces the problem to the invertibility of dS∘dS⁎ restricted to the subspace of functions corresponding to high Fourier modes. The inversion of such a restricted operator is finally achieved by making the crucial observation that lower order Fourier integral operators satisfy asymmetric tame estimates. |
| ArticleNumber | 109826 |
| Author | Benedetti, Gabriele Berti, Massimiliano Asselle, Luca |
| Author_xml | – sequence: 1 givenname: Luca surname: Asselle fullname: Asselle, Luca email: luca.asselle@rub.de organization: Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätsstraße 150, 44801 Bochum, Germany – sequence: 2 givenname: Gabriele surname: Benedetti fullname: Benedetti, Gabriele email: g.benedetti@vu.nl organization: Vrije Universiteit Amsterdam, Department of Mathematics, De Boelelaan 1111, 1081 HV Amsterdam, Netherlands – sequence: 3 givenname: Massimiliano surname: Berti fullname: Berti, Massimiliano email: berti@sissa.it organization: SISSA, Via Bonomea 265, 34136, Trieste, Italy |
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| Cites_doi | 10.4310/JSG.2022.v20.n1.a3 10.4310/jdg/1519959623 10.1088/1361-6544/ab839c 10.1112/blms/bdw050 10.1017/S0305004121000311 10.1007/s12220-020-00379-1 10.1007/BF00251855 10.1007/BF01449019 10.1007/s00039-014-0250-2 10.4310/jdg/1090351530 10.1007/BF01058438 10.1016/0001-8708(76)90139-0 10.4171/211 10.1007/s00039-023-00624-z 10.4171/pm/2039 10.1007/s00205-015-0842-5 10.5802/jep.231 10.4171/jems/361 10.1090/tran/8233 10.1007/s00222-017-0755-z 10.1007/BF01456044 10.1090/S0273-0979-1982-15004-2 |
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| Keywords | Hamiltonian systems Magnetic geodesics Nash–Moser implicit function theorem Zoll flows Fourier integral operators Bessel functions |
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| References | Ambrozio, Marques, Neves (br0060) 2021 Zoll (br0290) 1903; 57 Mazzucchelli, Suhr (br0260) 2022; 172 Tabachnikov (br0280) 2004 Benedetti (br0100) 2016; 48 Hörmander (br0220) 1976; 62 Guillemin (br0190) 1976; 22 Katz (br0230) 2007; vol. 137 Lochak (br0250) 1992; 47 Benedetti, Kang (br0110) 2020; 76 Abbondandolo, Bramham, Hryniewicz, Salomão (br0030) 2021; 374 Berti, Bolle (br0140) 2020 Berti, Bolle (br0130) 2013; 15 Asselle, Benedetti (br0070) 2021; 31 Lebrun, Mason (br0240) 2002; 61 Alazard, Baldi (br0040) 2015; 217 Hamilton (br0200) 1982; 7 Abbondandolo, Benedetti (br0010) 2023 Bambusi, Giorgilli (br0090) 1993; 71 Benedetti, Kang (br0120) 2022; 20 Besse (br0160) 1978; vol. 93 Funk (br0180) 1913; 74 Asselle, Lange (br0080) 2020; 33 Bohr, Paternain (br0170) 2023; 10 Stein (br0270) 1993 Berti, Montalto (br0150) 2020; 263 Álvarez Paiva, Balacheff (br0050) 2014; 24 Holman, Uhlmann (br0210) 2018; 108 Abbondandolo, Bramham, Hryniewicz, Salomão (br0020) 2018; 211 Abbondandolo (10.1016/j.aim.2024.109826_br0030) 2021; 374 Berti (10.1016/j.aim.2024.109826_br0140) 2020 Berti (10.1016/j.aim.2024.109826_br0150) 2020; 263 Hamilton (10.1016/j.aim.2024.109826_br0200) 1982; 7 Stein (10.1016/j.aim.2024.109826_br0270) 1993 Holman (10.1016/j.aim.2024.109826_br0210) 2018; 108 Ambrozio (10.1016/j.aim.2024.109826_br0060) Berti (10.1016/j.aim.2024.109826_br0130) 2013; 15 Mazzucchelli (10.1016/j.aim.2024.109826_br0260) 2022; 172 Álvarez Paiva (10.1016/j.aim.2024.109826_br0050) 2014; 24 Zoll (10.1016/j.aim.2024.109826_br0290) 1903; 57 Abbondandolo (10.1016/j.aim.2024.109826_br0010) 2023 Alazard (10.1016/j.aim.2024.109826_br0040) 2015; 217 Benedetti (10.1016/j.aim.2024.109826_br0100) 2016; 48 Tabachnikov (10.1016/j.aim.2024.109826_br0280) 2004 Hörmander (10.1016/j.aim.2024.109826_br0220) 1976; 62 Benedetti (10.1016/j.aim.2024.109826_br0120) 2022; 20 Bambusi (10.1016/j.aim.2024.109826_br0090) 1993; 71 Guillemin (10.1016/j.aim.2024.109826_br0190) 1976; 22 Abbondandolo (10.1016/j.aim.2024.109826_br0020) 2018; 211 Bohr (10.1016/j.aim.2024.109826_br0170) 2023; 10 Funk (10.1016/j.aim.2024.109826_br0180) 1913; 74 Lochak (10.1016/j.aim.2024.109826_br0250) 1992; 47 Katz (10.1016/j.aim.2024.109826_br0230) 2007; vol. 137 Asselle (10.1016/j.aim.2024.109826_br0070) 2021; 31 Besse (10.1016/j.aim.2024.109826_br0160) 1978; vol. 93 Asselle (10.1016/j.aim.2024.109826_br0080) 2020; 33 Benedetti (10.1016/j.aim.2024.109826_br0110) 2020; 76 Lebrun (10.1016/j.aim.2024.109826_br0240) 2002; 61 |
| References_xml | – volume: 61 start-page: 453 year: 2002 end-page: 535 ident: br0240 article-title: Zoll manifolds and complex surfaces publication-title: J. Differ. Geom. – volume: 76 start-page: 327 year: 2020 end-page: 394 ident: br0110 article-title: On a local systolic inequality for odd-symplectic forms publication-title: Port. Math. – volume: 7 start-page: 65 year: 1982 end-page: 222 ident: br0200 article-title: The inverse function theorem of Nash and Moser publication-title: Bull. Am. Math. Soc. (N. S.) – volume: 22 start-page: 85 year: 1976 end-page: 119 ident: br0190 article-title: The Radon transform on Zoll surfaces publication-title: Adv. Math. – volume: 374 start-page: 1815 year: 2021 end-page: 1845 ident: br0030 article-title: Sharp systolic inequalities for Riemannian and Finsler spheres of revolution publication-title: Trans. Am. Math. Soc. – volume: 24 start-page: 648 year: 2014 end-page: 669 ident: br0050 article-title: Contact geometry and isosystolic inequalities publication-title: Geom. Funct. Anal. – volume: 10 start-page: 727 year: 2023 end-page: 769 ident: br0170 article-title: The transport Oka–Grauert principle for simple surfaces publication-title: J. Éc. polytech. Math. – start-page: 233 year: 2004 end-page: 250 ident: br0280 article-title: Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem publication-title: Modern Dynamical Systems and Applications – volume: 57 start-page: 108 year: 1903 end-page: 133 ident: br0290 article-title: Über Flächen mit Scharen geschlossener geodätischer Linien publication-title: Math. Ann. – volume: 31 start-page: 2924 year: 2021 end-page: 2940 ident: br0070 article-title: Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities publication-title: J. Geom. Anal. – year: 2020 ident: br0140 article-title: Quasi-Periodic Solutions of Nonlinear Wave Equations on the publication-title: EMS Monographs in Mathematics – year: 1993 ident: br0270 article-title: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals – volume: 62 start-page: 1 year: 1976 end-page: 52 ident: br0220 article-title: The boundary problems of physical geodesy publication-title: Arch. Ration. Mech. Anal. – volume: vol. 93 year: 1978 ident: br0160 article-title: Manifolds All of Whose Geodesics Are Closed publication-title: Ergebnisse der Mathematik und Ihrer Grenzgebiete – volume: 20 start-page: 99 year: 2022 end-page: 134 ident: br0120 article-title: On a systolic inequality for closed magnetic geodesics on surfaces publication-title: J. Symplectic Geom. – volume: 172 start-page: 591 year: 2022 end-page: 615 ident: br0260 article-title: A min-max characterization of Zoll Riemannian metrics publication-title: Math. Proc. Camb. Philos. Soc. – volume: 217 start-page: 741 year: 2015 end-page: 830 ident: br0040 article-title: Gravity capillary standing water waves publication-title: Arch. Ration. Mech. Anal. – volume: 108 start-page: 459 year: 2018 end-page: 494 ident: br0210 article-title: On the microlocal analysis of the geodesic X-ray transform with conjugate points publication-title: J. Differ. Geom. – year: 2023 ident: br0010 article-title: On the local systolic optimality of Zoll contact forms publication-title: Geom. Funct. Anal. – volume: 48 start-page: 855 year: 2016 end-page: 865 ident: br0100 article-title: Magnetic Katok examples on the two-sphere publication-title: Bull. Lond. Math. Soc. – volume: 263 year: 2020 ident: br0150 article-title: Quasi-periodic standing wave solutions of gravity-capillary water waves publication-title: Mem. Am. Math. Soc. – volume: 33 start-page: 3173 year: 2020 end-page: 3194 ident: br0080 article-title: On the rigidity of Zoll magnetic systems on surfaces publication-title: Nonlinearity – volume: 211 start-page: 687 year: 2018 end-page: 778 ident: br0020 article-title: Sharp systolic inequalities for Reeb flows on the three-sphere publication-title: Invent. Math. – volume: vol. 137 year: 2007 ident: br0230 article-title: Systolic Geometry and Topology publication-title: Mathematical Surveys and Monographs – volume: 74 start-page: 278 year: 1913 end-page: 300 ident: br0180 article-title: Über Flächen mit lauter geschlossenen geodätischen Linien publication-title: Math. Ann. – volume: 15 start-page: 229 year: 2013 end-page: 286 ident: br0130 article-title: Quasi-periodic solutions with Sobolev regularity of NLS on publication-title: J. Eur. Math. Soc. – year: 2021 ident: br0060 article-title: Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces – volume: 47 start-page: 59 year: 1992 end-page: 140 ident: br0250 article-title: Canonical perturbation theory: an approach based on joint approximations publication-title: Usp. Mat. Nauk – volume: 71 start-page: 569 year: 1993 end-page: 606 ident: br0090 article-title: Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems publication-title: J. Stat. Phys. – volume: 20 start-page: 99 issue: 1 year: 2022 ident: 10.1016/j.aim.2024.109826_br0120 article-title: On a systolic inequality for closed magnetic geodesics on surfaces publication-title: J. Symplectic Geom. doi: 10.4310/JSG.2022.v20.n1.a3 – volume: 108 start-page: 459 issue: 3 year: 2018 ident: 10.1016/j.aim.2024.109826_br0210 article-title: On the microlocal analysis of the geodesic X-ray transform with conjugate points publication-title: J. Differ. Geom. doi: 10.4310/jdg/1519959623 – volume: 33 start-page: 3173 year: 2020 ident: 10.1016/j.aim.2024.109826_br0080 article-title: On the rigidity of Zoll magnetic systems on surfaces publication-title: Nonlinearity doi: 10.1088/1361-6544/ab839c – volume: 48 start-page: 855 issue: 5 year: 2016 ident: 10.1016/j.aim.2024.109826_br0100 article-title: Magnetic Katok examples on the two-sphere publication-title: Bull. Lond. Math. Soc. doi: 10.1112/blms/bdw050 – volume: vol. 93 year: 1978 ident: 10.1016/j.aim.2024.109826_br0160 article-title: Manifolds All of Whose Geodesics Are Closed – volume: 47 start-page: 59 issue: 6(288) year: 1992 ident: 10.1016/j.aim.2024.109826_br0250 article-title: Canonical perturbation theory: an approach based on joint approximations publication-title: Usp. Mat. Nauk – volume: 172 start-page: 591 issue: 3 year: 2022 ident: 10.1016/j.aim.2024.109826_br0260 article-title: A min-max characterization of Zoll Riemannian metrics publication-title: Math. Proc. Camb. Philos. Soc. doi: 10.1017/S0305004121000311 – volume: 31 start-page: 2924 year: 2021 ident: 10.1016/j.aim.2024.109826_br0070 article-title: Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities publication-title: J. Geom. Anal. doi: 10.1007/s12220-020-00379-1 – volume: 62 start-page: 1 issue: 1 year: 1976 ident: 10.1016/j.aim.2024.109826_br0220 article-title: The boundary problems of physical geodesy publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/BF00251855 – volume: 57 start-page: 108 year: 1903 ident: 10.1016/j.aim.2024.109826_br0290 article-title: Über Flächen mit Scharen geschlossener geodätischer Linien publication-title: Math. Ann. doi: 10.1007/BF01449019 – volume: 24 start-page: 648 issue: 2 year: 2014 ident: 10.1016/j.aim.2024.109826_br0050 article-title: Contact geometry and isosystolic inequalities publication-title: Geom. Funct. Anal. doi: 10.1007/s00039-014-0250-2 – volume: 61 start-page: 453 issue: 3 year: 2002 ident: 10.1016/j.aim.2024.109826_br0240 article-title: Zoll manifolds and complex surfaces publication-title: J. Differ. Geom. doi: 10.4310/jdg/1090351530 – volume: 71 start-page: 569 issue: 3–4 year: 1993 ident: 10.1016/j.aim.2024.109826_br0090 article-title: Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems publication-title: J. Stat. Phys. doi: 10.1007/BF01058438 – volume: 22 start-page: 85 year: 1976 ident: 10.1016/j.aim.2024.109826_br0190 article-title: The Radon transform on Zoll surfaces publication-title: Adv. Math. doi: 10.1016/0001-8708(76)90139-0 – year: 2020 ident: 10.1016/j.aim.2024.109826_br0140 article-title: Quasi-Periodic Solutions of Nonlinear Wave Equations on the d-Dimensional Torus doi: 10.4171/211 – start-page: 233 year: 2004 ident: 10.1016/j.aim.2024.109826_br0280 article-title: Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem – year: 2023 ident: 10.1016/j.aim.2024.109826_br0010 article-title: On the local systolic optimality of Zoll contact forms publication-title: Geom. Funct. Anal. doi: 10.1007/s00039-023-00624-z – volume: 76 start-page: 327 issue: 3–4 year: 2020 ident: 10.1016/j.aim.2024.109826_br0110 article-title: On a local systolic inequality for odd-symplectic forms publication-title: Port. Math. doi: 10.4171/pm/2039 – volume: 217 start-page: 741 issue: 3 year: 2015 ident: 10.1016/j.aim.2024.109826_br0040 article-title: Gravity capillary standing water waves publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-015-0842-5 – volume: 10 start-page: 727 year: 2023 ident: 10.1016/j.aim.2024.109826_br0170 article-title: The transport Oka–Grauert principle for simple surfaces publication-title: J. Éc. polytech. Math. doi: 10.5802/jep.231 – volume: 15 start-page: 229 issue: 1 year: 2013 ident: 10.1016/j.aim.2024.109826_br0130 article-title: Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential publication-title: J. Eur. Math. Soc. doi: 10.4171/jems/361 – volume: 374 start-page: 1815 issue: 3 year: 2021 ident: 10.1016/j.aim.2024.109826_br0030 article-title: Sharp systolic inequalities for Riemannian and Finsler spheres of revolution publication-title: Trans. Am. Math. Soc. doi: 10.1090/tran/8233 – year: 1993 ident: 10.1016/j.aim.2024.109826_br0270 – volume: 263 issue: 1273 year: 2020 ident: 10.1016/j.aim.2024.109826_br0150 article-title: Quasi-periodic standing wave solutions of gravity-capillary water waves publication-title: Mem. Am. Math. Soc. – volume: 211 start-page: 687 issue: 2 year: 2018 ident: 10.1016/j.aim.2024.109826_br0020 article-title: Sharp systolic inequalities for Reeb flows on the three-sphere publication-title: Invent. Math. doi: 10.1007/s00222-017-0755-z – ident: 10.1016/j.aim.2024.109826_br0060 – volume: 74 start-page: 278 year: 1913 ident: 10.1016/j.aim.2024.109826_br0180 article-title: Über Flächen mit lauter geschlossenen geodätischen Linien publication-title: Math. Ann. doi: 10.1007/BF01456044 – volume: vol. 137 year: 2007 ident: 10.1016/j.aim.2024.109826_br0230 article-title: Systolic Geometry and Topology – volume: 7 start-page: 65 issue: 1 year: 1982 ident: 10.1016/j.aim.2024.109826_br0200 article-title: The inverse function theorem of Nash and Moser publication-title: Bull. Am. Math. Soc. (N. S.) doi: 10.1090/S0273-0979-1982-15004-2 |
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| SubjectTerms | Bessel functions Fourier integral operators Hamiltonian systems Magnetic geodesics Nash–Moser implicit function theorem Zoll flows |
| Title | Zoll magnetic systems on the two-torus: A Nash–Moser construction |
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