Trace Formula for Linear Hamiltonian Systems with its Applications to Elliptic Lagrangian Solutions
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0810-5 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0810-5 | ||
| 245 | 0 | 0 | |a Trace Formula for Linear Hamiltonian Systems with its Applications to Elliptic Lagrangian Solutions |h [Elektronische Daten] |c [Xijun Hu, Yuwei Ou, Penghui Wang] |
| 520 | 3 | |a In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the Hessian of the action functional. A natural application is to study the non-degeneracy of linear Hamiltonian systems. Precisely, by the trace formula, we can give an estimation for the upper bound such that the non-degeneracy preserves. Moreover, we could estimate the relative Morse index by the trace formula. Consequently, a series of new stability criteria for the symmetric periodic orbits is given. As a concrete application, the trace formula is used to study the linear stability of elliptic Lagrangian solutions of the classical planar three-body problem, which depends on the mass parameter $${\beta \in [0,9]}$$ β ∈ [ 0 , 9 ] and the eccentricity $${e \in [0,1)}$$ e ∈ [ 0 , 1 ) . Based on the trace formula, we estimate the stable region and hyperbolic region of the elliptic Lagrangian solutions. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Hu |D Xijun |u Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China |4 aut | |
| 700 | 1 | |a Ou |D Yuwei |u Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China |4 aut | |
| 700 | 1 | |a Wang |D Penghui |u Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/1(2015-04-01), 313-357 |x 0003-9527 |q 216:1<313 |1 2015 |2 216 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0810-5 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0810-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hu |D Xijun |u Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ou |D Yuwei |u Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wang |D Penghui |u Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/1(2015-04-01), 313-357 |x 0003-9527 |q 216:1<313 |1 2015 |2 216 |o 205 | ||