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【期刊论文】Index Iteration Theory for Symplectic Paths with Applications to Nonlinear Hamiltonian Systems
龙以明, Yiming Long*
This paper is published in Proc. of Inter. Congress of Math. 2002 Vol.11, 303-313.,-0001,():
-1年11月30日
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.
Iteration theory,, Index,, Symplectic path,, Hamiltonian system,, Periodic orbit.,
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【期刊论文】Multiple periodic points of the Poincar
龙以明, Yiming Long,
This paper is published in Math. Z. Vol. 233 (2000)443-470.,-0001,():
-1年11月30日
In this paper, suppose L(t,x,p) =12A(x)p·p + V (t, x), A is positive definite and symmetric, and both A and V are C3 and 1-periodic in all of their variables. We prove that the Poincare map (i.e. the time-1-solution map) of the Lagrangian system d dt Lx˙(t, x, x˙)−Lx(t, x, x˙) =0 possesses infinitely many periodic points on Tn produced by contractible integer periodic solutions.
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【期刊论文】Hyperbolic closed characteristics on compact convex smooth hypersurfaces in R2n
龙以明, Yiming Long,
This paper is published in J. Diff. Eqns. Vol. 150 (1998), 227-249.,-0001,():
-1年11月30日
In this paper we prove that on every compact C2 hypersurface in R2n bounding a convex set with non-empty interior, either there exists a sequence of variationally visible hyperbolic closed characteristcs with their minimal periods tending to infinity, or there exists at least one variationally visible nonhyperbolic closed characteristic.
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【期刊论文】Closed characteristics on compact convex hypersurfaces in R2n
龙以明, Yiming Long*† and Chaofeng Zhu‡
This paper is published in Annals of Mathematics 155 (2) (2002),317-368.,-0001,():
-1年11月30日
For any given compact C2 hypersurface
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【期刊论文】Multiplicity of closed characteristics on symmetric convex hypersurfaces in R2n
龙以明, Chun-gen Liu*, and Yiming Long, y†‡ Chaofeng Zhuξ
This paper is published in Math. Ann. Vol. 323 (2002), 201-215.,-0001,():
-1年11月30日
Let
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