Almost periodic transformable difference systems

Abstract We analyse almost periodic homogeneous linear difference systems whose coefficient matrices belong to the so-called transformable groups. We introduce the notion of weakly transformable groups and we use this notion to obtain generalizations of known results about non-almost periodic solutions of considered systems.

[1]  Jialin Hong,et al.  The existence of almost periodic solutions for a class of differential equations with piecewise constant argument , 1997 .

[2]  Héctor J. Sussmann,et al.  Construction of ergodic cocycles that are fundamental solutions to linear systems of a special form , 2007 .

[3]  A. V. Lipnitskii On the singular and higher characteristic exponents of an almost periodic linear differential system with an affine dependence on a parameter , 2006 .

[4]  Héctor J. Sussmann,et al.  Construction of minimal cocycles arising from specific differential equations , 1997 .

[5]  W. Greub Linear Algebra , 1981 .

[6]  R. K. Romanovskii,et al.  The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients , 2010 .

[7]  Hermitian symplectic geometry and extension theory , 2000, math-ph/0703027.

[8]  N. T. Thành,et al.  Asymptotically almost periodic solutions on the half-line , 2005 .

[9]  Michal Veselý,et al.  Construction of almost periodic functions with given properties , 2011 .

[10]  A. Fink Almost Periodic Differential Equations , 1974 .

[11]  RenZiYANG,et al.  Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients , 2004 .

[12]  Daniel M. Dunlavy,et al.  Structure Preserving Algorithms for Perplectic Eigenproblems , 2005 .

[13]  Kondalsamy Gopalsamy,et al.  Almost Periodic Solutions of Nonautonomous Linear Difference Equations , 2002 .

[14]  A. S. Kotyurgina,et al.  The method of Lyapunov functions for systems of linear difference equations with almost periodic coefficients , 1996 .

[15]  Constantin Corduneanu,et al.  Almost Periodic Oscillations and Waves , 2008 .

[16]  Michal Veselý,et al.  Construction of almost periodic sequences with given properties , 2008 .

[17]  Andrej Muchnik,et al.  Almost periodic sequences , 2003, Theor. Comput. Sci..

[18]  Shunian Zhang,et al.  Almost periodic solutions of difference systems , 1998 .

[19]  Michal Veselý,et al.  Almost periodic homogeneous linear difference systems without almost periodic solutions , 2012 .

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

[21]  Vimal Singh,et al.  Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  H. Georgi,et al.  Unity of All Elementary Particle Forces , 1974 .

[23]  Guang Zheng,et al.  Almost periodic solutions of delay difference systems , 2002, Appl. Math. Comput..

[24]  R. Yuan On Favard's theorems , 2010 .

[25]  Z. Alsharawi,et al.  Linear almost periodic difference equations , 2008 .

[26]  Xiao Wang,et al.  Globally dynamical behaviors for a class of nonlinear functional difference equation with almost periodic coefficients , 2007, Appl. Math. Comput..

[27]  V. I. Tkachenko,et al.  On linear almost periodic systems with bounded solutions , 1997, Bulletin of the Australian Mathematical Society.

[28]  E. A. Dads,et al.  Pseudo almost periodic solutions for equation with piecewise constant argument , 2010 .

[29]  Luigi Amerio,et al.  Almost-periodic functions and functional equations , 1971 .

[30]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[31]  V. Tkachenko,et al.  On linear systems with quasiperiodic coefficients and bounded solutions , 1996 .

[32]  W. A. Coppel Dichotomies in Stability Theory , 1978 .

[33]  A. V. Lipnitskii,et al.  On the discontinuity of lyapunov exponents of an almost periodic linear differential system affinely depending on a parameter , 2008 .

[34]  Garyfalos Papaschinopoulos Exponential separation, exponential dichotomy, and almost periodicity of linear difference equations , 1986 .

[35]  Tomás Caraballo,et al.  Almost periodic and almost automorphic solutions of linear differential equations , 2012 .

[36]  张书年 EXISTENCE OF ALMOST PERIODIC SOLUTIONS FOR DIFFERENCE SYSTEMS , 2000 .