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A generalized shadowing lemma
On the renormalization of Hamiltonian flows, and critical invariant tori
1. | Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, United States |
[1] |
Hans Koch, Héctor E. Lomelí. On Hamiltonian flows whose orbits are straight lines. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2091-2104. doi: 10.3934/dcds.2014.34.2091 |
[2] |
Yong Ji, Ercai Chen, Yunping Wang, Cao Zhao. Bowen entropy for fixed-point free flows. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6231-6239. doi: 10.3934/dcds.2019271 |
[3] |
Gernot Greschonig. Real cocycles of point-distal minimal flows. Conference Publications, 2015, 2015 (special) : 540-548. doi: 10.3934/proc.2015.0540 |
[4] |
Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807 |
[5] |
Denis G. Gaidashev. Renormalization of isoenergetically degenerate hamiltonian flows and associated bifurcations of invariant tori. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 63-102. doi: 10.3934/dcds.2005.13.63 |
[6] |
César J. Niche. Non-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 617-630. doi: 10.3934/dcds.2006.14.617 |
[7] |
Dou Dou, Meng Fan, Hua Qiu. Topological entropy on subsets for fixed-point free flows. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6319-6331. doi: 10.3934/dcds.2017273 |
[8] |
Gianluca Crippa, Milton C. Lopes Filho, Evelyne Miot, Helena J. Nussenzveig Lopes. Flows of vector fields with point singularities and the vortex-wave system. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2405-2417. doi: 10.3934/dcds.2016.36.2405 |
[9] |
Xavier Perrot, Xavier Carton. Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 971-995. doi: 10.3934/dcdsb.2009.11.971 |
[10] |
Tiphaine Jézéquel, Patrick Bernard, Eric Lombardi. Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3153-3225. doi: 10.3934/dcds.2016.36.3153 |
[11] |
Yuri B. Suris. Variational formulation of commuting Hamiltonian flows: Multi-time Lagrangian 1-forms. Journal of Geometric Mechanics, 2013, 5 (3) : 365-379. doi: 10.3934/jgm.2013.5.365 |
[12] |
Calin Iulian Martin. A Hamiltonian approach for nonlinear rotational capillary-gravity water waves in stratified flows. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 387-404. doi: 10.3934/dcds.2017016 |
[13] |
Kenneth R. Meyer, Jesús F. Palacián, Patricia Yanguas. Normally stable hamiltonian systems. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1201-1214. doi: 10.3934/dcds.2013.33.1201 |
[14] |
Hassan Najafi Alishah, Pedro Duarte. Hamiltonian evolutionary games. Journal of Dynamics and Games, 2015, 2 (1) : 33-49. doi: 10.3934/jdg.2015.2.33 |
[15] |
Antonio Giorgilli. Unstable equilibria of Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 855-871. doi: 10.3934/dcds.2001.7.855 |
[16] |
G. A. Swarup. On the cut point conjecture. Electronic Research Announcements, 1996, 2: 98-100. |
[17] |
Marek Rychlik. The Equichordal Point Problem. Electronic Research Announcements, 1996, 2: 108-123. |
[18] |
Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 |
[19] |
V. Barbu. Periodic solutions to unbounded Hamiltonian system. Discrete and Continuous Dynamical Systems, 1995, 1 (2) : 277-283. doi: 10.3934/dcds.1995.1.277 |
[20] |
P. Balseiro, M. de León, Juan Carlos Marrero, D. Martín de Diego. The ubiquity of the symplectic Hamiltonian equations in mechanics. Journal of Geometric Mechanics, 2009, 1 (1) : 1-34. doi: 10.3934/jgm.2009.1.1 |
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