American Institute of Mathematical Sciences

Advanced
April  2005, 13(3): 623-635. doi: 10.3934/dcds.2005.13.623

A perturbation theorem for linear Hamiltonian systems with bounded orbits

Roberta Fabbri 1, , Carmen Núñez 2, and  Ana M. Sanz 3,

1. 

Università di Firenze, Dipartimento di Sistemi e Informatica, Via Santa Marta 3, 50139 Firenze
2. 

Universidad de Valladolid, Departamento de Matemática Aplicada, ETSII, Paseo del Cauce s/n, 47011 Valladolid
3. 

Universidad de Valladolid, Departamento de Análisis Matemático y Didáctica de la Matemática, Prado de la Magdalena s/n, 47005 Valladolid, Spain

Received  August 2004 Revised  February 2005 Published  May 2005

This paper concerns the Sacker-Sell spectral decomposition of a one-parametric perturbation of a non-autonomous linear Hamiltonian system with bounded solutions. Conditions ensuring the continuous variation with respect to the parameter of the spectral intervals and subbundles are established. These conditions depend on the perturbation direction and are closely related to the topological structure of the flows induced by the initial system on the real and complex Lagrange bundles.
Keywords: Linear Hamiltonian systems, Sacker-Sell spectral decomposition, perturbation theorems..
Mathematics Subject Classification: Primary 37B55, 34D08; Secondary 34C11, 37D2.
Citation: Roberta Fabbri, Carmen Núñez, Ana M. Sanz. A perturbation theorem for linear Hamiltonian systems with bounded orbits. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 623-635. doi: 10.3934/dcds.2005.13.623
[1]

Roman Šimon Hilscher. On general Sturmian theory for abnormal linear Hamiltonian systems. Conference Publications, 2011, 2011 (Special) : 684-691. doi: 10.3934/proc.2011.2011.684
[2]

Galina Kurina, Sahlar Meherrem. Decomposition of discrete linear-quadratic optimal control problems for switching systems. Conference Publications, 2015, 2015 (special) : 764-774. doi: 10.3934/proc.2015.0764
[3]

Álvaro Castañeda, Gonzalo Robledo. Almost reducibility of linear difference systems from a spectral point of view. Communications on Pure & Applied Analysis, 2017, 16 (6) : 1977-1988. doi: 10.3934/cpaa.2017097
[4]

Mahesh G. Nerurkar. Spectral and stability questions concerning evolution of non-autonomous linear systems. Conference Publications, 2001, 2001 (Special) : 270-275. doi: 10.3934/proc.2001.2001.270
[5]

Qinqin Zhang. Homoclinic orbits for discrete Hamiltonian systems with indefinite linear part. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1929-1940. doi: 10.3934/cpaa.2015.14.1929
[6]

Peter Šepitka. Riccati equations for linear Hamiltonian systems without controllability condition. Discrete & Continuous Dynamical Systems, 2019, 39 (4) : 1685-1730. doi: 10.3934/dcds.2019074
[7]

Björn Augner, Birgit Jacob. Stability and stabilization of infinite-dimensional linear port-Hamiltonian systems. Evolution Equations & Control Theory, 2014, 3 (2) : 207-229. doi: 10.3934/eect.2014.3.207
[8]

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
[9]

Mark A. Pinsky, Alexandr A. Zevin. Stability criteria for linear Hamiltonian systems with uncertain bounded periodic coefficients. Discrete & Continuous Dynamical Systems, 2005, 12 (2) : 243-250. doi: 10.3934/dcds.2005.12.243
[10]

Vladimir Răsvan. On the central stability zone for linear discrete-time Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 734-741. doi: 10.3934/proc.2003.2003.734
[11]

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
[12]

Woochul Jung, Ngocthach Nguyen, Yinong Yang. Spectral decomposition for rescaling expansive flows with rescaled shadowing. Discrete & Continuous Dynamical Systems, 2020, 40 (4) : 2267-2283. doi: 10.3934/dcds.2020113
[13]

Keonhee Lee, Ngoc-Thach Nguyen, Yinong Yang. Topological stability and spectral decomposition for homeomorphisms on noncompact spaces. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2487-2503. doi: 10.3934/dcds.2018103
[14]

Guangcun Lu. Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021155
[15]

Matteo Petrera, Yuri B. Suris. Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. Ⅱ. Systems with a linear Poisson tensor. Journal of Computational Dynamics, 2019, 6 (2) : 401-408. doi: 10.3934/jcd.2019020
[16]

Christian Pötzsche, Stefan Siegmund, Fabian Wirth. A spectral characterization of exponential stability for linear time-invariant systems on time scales. Discrete & Continuous Dynamical Systems, 2003, 9 (5) : 1223-1241. doi: 10.3934/dcds.2003.9.1223
[17]

Victor Kozyakin. Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3537-3556. doi: 10.3934/dcdsb.2018277
[18]

Yuzhou Tian, Yulin Zhao. Global phase portraits and bifurcation diagrams for reversible equivariant Hamiltonian systems of linear plus quartic homogeneous polynomials. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2941-2956. doi: 10.3934/dcdsb.2020214
[19]

Jaume Llibre, Y. Paulina Martínez, Claudio Vidal. Linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 887-912. doi: 10.3934/dcdsb.2018047
[20]

Nathanael Skrepek. Well-posedness of linear first order port-Hamiltonian Systems on multidimensional spatial domains. Evolution Equations & Control Theory, 2021, 10 (4) : 965-1006. doi: 10.3934/eect.2020098

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (65)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences