Almost periodic homogeneous linear difference systems without almost periodic solutions

2012 ◽  
Vol 18 (10) ◽  
pp. 1623-1647 ◽  
Author(s):  
Michal Veselý
Keyword(s):  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Difference Systems ◽  
Homogeneous Linear ◽  
Linear Difference Systems

Values of limit periodic sequences and functions

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Michal Veselý ◽  
Petr Hasil
Keyword(s):  
Periodic Solutions ◽  
Periodic Sequence ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Periodic Sequences ◽  
Totally Bounded ◽  
Difference Systems

AbstractWe consider limit periodic sequences and functions with values in pseudometric spaces. We construct limit periodic sequences and functions with given values. For any totally bounded countable set, we find a limit periodic sequence which attains each value from this set periodically. A corresponding result concerning such a construction of limit periodic functions is proved as well. For any totally bounded countable set which is dense in itself, we construct a limit periodic bijective map from the integers into this set. As corollaries, we obtain new results about non-almost periodic solutions of almost periodic transformable difference systems.

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