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A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems
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Quasiperiodic motion for the pentagram map
1. | CNRS, Institut Camille Jordan, Université Lyon 1, Villeurbanne Cedex 69622, France |
2. | Department of Mathematics, Brown University, Providence, RI 02912, United States |
3. | Department of Mathematics, Penn State University, University Park, PA 16802 |
[1] |
Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159 |
[2] |
Carlos Durán, Diego Otero. The projective Cartan-Klein geometry of the Helmholtz conditions. Journal of Geometric Mechanics, 2018, 10 (1) : 69-92. doi: 10.3934/jgm.2018003 |
[3] |
Daniel Genin, Serge Tabachnikov. On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards. Journal of Modern Dynamics, 2007, 1 (2) : 155-173. doi: 10.3934/jmd.2007.1.155 |
[4] |
Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 |
[5] |
Carlos Durán, Diego Otero. The projective symplectic geometry of higher order variational problems: Minimality conditions. Journal of Geometric Mechanics, 2016, 8 (3) : 305-322. doi: 10.3934/jgm.2016009 |
[6] |
Miguel Ángel Evangelista-Alvarado, José Crispín Ruíz-Pantaleón, Pablo Suárez-Serrato. On computational Poisson geometry II: Numerical methods. Journal of Computational Dynamics, 2021, 8 (3) : 273-307. doi: 10.3934/jcd.2021012 |
[7] |
Miguel Ángel Evangelista-Alvarado, José Crispín Ruíz-Pantaleón, Pablo Suárez-Serrato. On computational Poisson geometry I: Symbolic foundations. Journal of Geometric Mechanics, 2021, 13 (4) : 607-628. doi: 10.3934/jgm.2021018 |
[8] |
Joachim Escher, Boris Kolev, Marcus Wunsch. The geometry of a vorticity model equation. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1407-1419. doi: 10.3934/cpaa.2012.11.1407 |
[9] |
Scott Crass. Solving the heptic by iteration in two dimensions: Geometry and dynamics under Klein's group of order 168. Journal of Modern Dynamics, 2007, 1 (2) : 175-203. doi: 10.3934/jmd.2007.1.175 |
[10] |
Sasho Popov, Jean-Marie Strelcyn. The Euler-Poisson equations: An elementary approach to integrability conditions. Journal of Geometric Mechanics, 2018, 10 (3) : 293-329. doi: 10.3934/jgm.2018011 |
[11] |
Mike Crampin, David Saunders. Homogeneity and projective equivalence of differential equation fields. Journal of Geometric Mechanics, 2012, 4 (1) : 27-47. doi: 10.3934/jgm.2012.4.27 |
[12] |
Daniele Bartoli, Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. Multiple coverings of the farthest-off points with small density from projective geometry. Advances in Mathematics of Communications, 2015, 9 (1) : 63-85. doi: 10.3934/amc.2015.9.63 |
[13] |
Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 |
[14] |
Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223 |
[15] |
Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73 |
[16] |
Q-Heung Choi, Changbum Chun, Tacksun Jung. The multiplicity of solutions and geometry in a wave equation. Communications on Pure and Applied Analysis, 2003, 2 (2) : 159-170. doi: 10.3934/cpaa.2003.2.159 |
[17] |
Tomoki Ohsawa, Anthony M. Bloch. Nonholonomic Hamilton-Jacobi equation and integrability. Journal of Geometric Mechanics, 2009, 1 (4) : 461-481. doi: 10.3934/jgm.2009.1.461 |
[18] |
Larry M. Bates, Francesco Fassò, Nicola Sansonetto. The Hamilton-Jacobi equation, integrability, and nonholonomic systems. Journal of Geometric Mechanics, 2014, 6 (4) : 441-449. doi: 10.3934/jgm.2014.6.441 |
[19] |
Gunter M. Ziegler. Projected products of polygons. Electronic Research Announcements, 2004, 10: 122-134. |
[20] |
Simon Castle, Norbert Peyerimhoff, Karl Friedrich Siburg. Billiards in ideal hyperbolic polygons. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 893-908. doi: 10.3934/dcds.2011.29.893 |
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