caa a22 4500 60551500X CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00205-014-0810-5 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0810-5 Trace Formula for Linear Hamiltonian Systems with its Applications to Elliptic Lagrangian Solutions [Elektronische Daten] [Xijun Hu, Yuwei Ou, Penghui Wang] 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. Springer-Verlag Berlin Heidelberg, 2014 Hu Xijun Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China aut Ou Yuwei Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China aut Wang Penghui Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 313-357 0003-9527 216:1<313 2015 216 205 https://doi.org/10.1007/s00205-014-0810-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0810-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hu Xijun Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China aut NATIONALLICENCE 700 1- Ou Yuwei Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China aut NATIONALLICENCE 700 1- Wang Penghui Department of Mathematics, Shandong University Jinan, 250100, Shandong, The People's Republic of China aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 313-357 0003-9527 216:1<313 2015 216 205