On Polynomial Dichotomy of Linear Discrete-Time Systems in Banach Spaces
Received:September 15, 2014  Revised:March 09, 2015
Key Words: linear discrete-time systems   uniform polynomial dichotomy   polynomial dichotomy  
Fund Project:Supported by the Fundamental Research Funds for the Central Universities (Grant No.2012LWB53) and the Natural Science Foundation of Hubei Province (Grant No.2014CFB629).
Author NameAffiliation
Tian YUE School of Science, Hubei University of Automotive Technology, Hubei 442002, P. R. China 
Guoliang LEI School of Science, Hubei University of Automotive Technology, Hubei 442002, P. R. China 
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Abstract:
      This paper deals with two concepts of polynomial dichotomy for linear difference equations which are defined in a Banach space and whose norms can increase not faster than exponentially. Some illustrating examples clarify the relations between these concepts. Our approach is based on the extension of techniques for exponential dichotomy to the case of polynomial dichotomy. The obtained results are generalizations of well-known theorems about the exponential stability and exponential dichotomy.
Citation:
DOI:10.3770/j.issn:2095-2651.2015.05.007
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