典型文献
Brake Orbits of a Reversible Even Hamiltonian System Near an Equilibrium
文献摘要：
In this paper,we consider the brake orbits of a reversible even Hamiltonian system near an equilibrium.Let the Hamiltonian system(HS)(x)=JH′(x)satisfies H(0)=0,H′(0)=0,reversible and even conditions H(Nx)=H(x)and H(-x)=H(x)for all x ∈ R2n.Suppose the quadratic form Q(x)=1/2is non-degenerate.Fix τ0＞0 and assume that R2n=E ⊕ F decomposes into linear subspaces E and F which are invariant under the flow associated to the linear system x=JH″(0)x and such that each solution of the above linear system in E is r0-periodic whereas no solution in F \{0}is τ0-periodic.Write σ(τ0)=σQ(τ0)for the signature of Q|E.If σ(τ0)≠ 0,we prove that either there exists a sequence of brake orbits xk → 0 with τk-periodic on the hypersurface H-1(0)where τk → τ0;or for each λ close to 0 with λσ(τ0)＞0 the hypersurface H-1(λ)contains at least 1/2|σ(τ0)| distinct brake orbits of the Hamiltonian system(HS)near 0 with periods near τ0.Such result for periodic solutions was proved by Bartsch in 1997.
文献关键词：
中图分类号：
作者姓名：
Zhong Jie LIU;Fan Jing WANG;Duan Zhi ZHANG
作者机构：
School of Science,Tianjin Chengjian University,Tianjin 300384,P.R.China;School of Mathematics and Statistics,Shanghai Lixin University of Accounting and Finance,Shanghai 201209,P.R.China;School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China
文献出处：
引用格式：
[1]Zhong Jie LIU;Fan Jing WANG;Duan Zhi ZHANG-.Brake Orbits of a Reversible Even Hamiltonian System Near an Equilibrium)[J].数学学报（英文版）,2022(01):263-280
A类：
R2n,Bartsch
B类：
Brake,Orbits,Reversible,Even,Hamiltonian,System,Near,Equilibrium,In,this,paper,we,consider,brake,orbits,reversible,even,system,equilibrium,Let,HS,JH,satisfies,conditions,Nx,all,Suppose,quadratic,form,degenerate,Fix,assume,that,decomposes,into,linear,subspaces,which,are,invariant,under,flow,associated,such,each,above,r0,periodic,whereas,Write,signature,If,either,there,exists,sequence,xk,hypersurface,close,contains,least,distinct,periods,Such,result,solutions,was,proved,by
AB值：
0.557906
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