论文信息 - Mean Index for Non-periodic Orbits in Hamiltonian Systems

Mean Index for Non-periodic Orbits in Hamiltonian Systems

In this paper, we define mean index for non-periodic orbits in Hamiltonian systems and study its properties. In general, the mean index is an interval in ℝ which is uniformly continuous on the systems. We show that the index interval is a point for a quasi-periodic orbit. The mean index can be considered as a generalization of rotation number defined by Johnson and Moser in the study of almost periodic Schrödinger operators. Motivated by their works, we study the relation of Fredholm property of the linear operator and the mean index at the end of the paper.

Li Wu | Xijun Hu | Li Wu | Xijun Hu

[1] P. Walters. Introduction to Ergodic Theory , 1977 .

[2] N. G. Parke,et al. Ordinary Differential Equations. , 1958 .

[3] Joel W. Robbin,et al. The Maslov index for paths , 1993 .

[4] Shanzhong Sun,et al. Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit , 2009 .

[5] Li Wu,et al. Hörmander index in finite-dimensional case , 2018 .

[6] A. Portaluri,et al. Index theory for heteroclinic orbits of Hamiltonian systems , 2017, 1703.03908.

[7] Berna Yilmaz,et al. 207 , 2019, Critical Care Medicine.

[8] I. Ekeland. Convexity Methods In Hamiltonian Mechanics , 1990 .

[9] J. Moser,et al. The rotation number for almost periodic potentials , 1982 .

[10] Shanshan Tang,et al. Maslov (P, ω)-Index Theory for Symplectic Paths , 2015 .

[11] Joel W. Robbin,et al. The Spectral Flow and the Maslov Index , 1995 .

[12] M. Mirzakhani,et al. Introduction to Ergodic theory , 2010 .

[13] Y. Long,et al. Maslov-Type Index Theory for Symplectic Paths and Spectral Flow (II) , 1980 .

[14] Kenneth J. Palmer,et al. Exponential dichotomies and Fredholm operators , 1988 .

[15] H. Furstenberg,et al. Strict Ergodicity and Transformation of the Torus , 1961 .

[16] Y. Long. Index Theory for Symplectic Paths with Applications , 2002 .