American Institute of Mathematical Sciences

Advanced
July  1995, 1(3): 389-400. doi: 10.3934/dcds.1995.1.389

Critical values and minimal periods for autonomous Hamiltonian systems

K. Tintarev 1,

1. 

Uppsala University, Box 480, Uppsala 751 06, Sweden

Received  January 1995 Published  May 1995

The paper studies periodic solutions of Hamiltonian systems. It states that a range of periods for such solutions can be obtained by diiferentiation of the function of constrained critical values with respect to the variable constraint level. It also shows that when a Hamiltonian is equal to a positive quadratic form plus an oscillatory term, there exist infinitely many solutions with the same period.
Keywords: periodic solutions, Hamiltonian systems, critical values..
Mathematics Subject Classification: 37J45, 70H0.
Citation: K. Tintarev. Critical values and minimal periods for autonomous Hamiltonian systems. Discrete & Continuous Dynamical Systems, 1995, 1 (3) : 389-400. doi: 10.3934/dcds.1995.1.389
[1]

Tianqing An, Zhi-Qiang Wang. Periodic solutions of Hamiltonian systems with anisotropic growth. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1069-1082. doi: 10.3934/cpaa.2010.9.1069
[2]

Alessandro Fonda, Andrea Sfecci. Multiple periodic solutions of Hamiltonian systems confined in a box. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1425-1436. doi: 10.3934/dcds.2017059
[3]

Anna Capietto, Walter Dambrosio, Tiantian Ma, Zaihong Wang. Unbounded solutions and periodic solutions of perturbed isochronous Hamiltonian systems at resonance. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 1835-1856. doi: 10.3934/dcds.2013.33.1835
[4]

Jianshe Yu, Honghua Bin, Zhiming Guo. Periodic solutions for discrete convex Hamiltonian systems via Clarke duality. Discrete & Continuous Dynamical Systems, 2006, 15 (3) : 939-950. doi: 10.3934/dcds.2006.15.939
[5]

Pietro-Luciano Buono, Daniel C. Offin. Instability criterion for periodic solutions with spatio-temporal symmetries in Hamiltonian systems. Journal of Geometric Mechanics, 2017, 9 (4) : 439-457. doi: 10.3934/jgm.2017017
[6]

Mitsuru Shibayama. Periodic solutions for a prescribed-energy problem of singular Hamiltonian systems. Discrete & Continuous Dynamical Systems, 2017, 37 (5) : 2705-2715. doi: 10.3934/dcds.2017116
[7]

Shiwang Ma. Nontrivial periodic solutions for asymptotically linear hamiltonian systems at resonance. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2361-2380. doi: 10.3934/cpaa.2013.12.2361
[8]

Laura Olian Fannio. Multiple periodic solutions of Hamiltonian systems with strong resonance at infinity. Discrete & Continuous Dynamical Systems, 1997, 3 (2) : 251-264. doi: 10.3934/dcds.1997.3.251
[9]

Liang Ding, Rongrong Tian, Jinlong Wei. Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1617-1625. doi: 10.3934/dcdsb.2018222
[10]

Paolo Gidoni, Alessandro Margheri. Lower bound on the number of periodic solutions for asymptotically linear planar Hamiltonian systems. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 585-606. doi: 10.3934/dcds.2019024
[11]

Giuseppe Cordaro. Existence and location of periodic solutions to convex and non coercive Hamiltonian systems. Discrete & Continuous Dynamical Systems, 2005, 12 (5) : 983-996. doi: 10.3934/dcds.2005.12.983
[12]

Ernest Fontich, Rafael de la Llave, Yannick Sire. A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Electronic Research Announcements, 2009, 16: 9-22. doi: 10.3934/era.2009.16.9
[13]

Stéphane Chrétien, Sébastien Darses, Christophe Guyeux, Paul Clarkson. On the pinning controllability of complex networks using perturbation theory of extreme singular values. application to synchronisation in power grids. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 289-299. doi: 10.3934/naco.2017019
[14]

V. Barbu. Periodic solutions to unbounded Hamiltonian system. Discrete & Continuous Dynamical Systems, 1995, 1 (2) : 277-283. doi: 10.3934/dcds.1995.1.277
[15]

Xiao-Fei Zhang, Fei Guo. Multiplicity of subharmonic solutions and periodic solutions of a particular type of super-quadratic Hamiltonian systems. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1625-1642. doi: 10.3934/cpaa.2016005
[16]

Chungen Liu, Xiaofei Zhang. Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1559-1574. doi: 10.3934/dcds.2017064
[17]

Xingyong Zhang, Xianhua Tang. Some united existence results of periodic solutions for non-quadratic second order Hamiltonian systems. Communications on Pure & Applied Analysis, 2014, 13 (1) : 75-95. doi: 10.3934/cpaa.2014.13.75
[18]

Jia Li, Junxiang Xu. On the reducibility of a class of almost periodic Hamiltonian systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3905-3919. doi: 10.3934/dcdsb.2020268
[19]

Manassés de Souza. On a singular Hamiltonian elliptic systems involving critical growth in dimension two. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1859-1874. doi: 10.3934/cpaa.2012.11.1859
[20]

Rumei Zhang, Jin Chen, Fukun Zhao. Multiple solutions for superlinear elliptic systems of Hamiltonian type. Discrete & Continuous Dynamical Systems, 2011, 30 (4) : 1249-1262. doi: 10.3934/dcds.2011.30.1249

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (49)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences