Displaying similar documents to “On periodic mod p sequences and G-functions (On a conjecture of Ruzsa).”

Partially irregular almost periodic solutions of ordinary differential systems

Alexandr Demenchuk (2001)

Mathematica Bohemica

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Let f ( t , x ) be a vector valued function almost periodic in t uniformly for x , and let m o d ( f ) = L 1 L 2 be its frequency module. We say that an almost periodic solution x ( t ) of the system x ˙ = f ( t , x ) , t , x D n is irregular with respect to L 2 (or partially irregular) if ( m o d ( x ) + L 1 ) L 2 = { 0 } . Suppose that f ( t , x ) = A ( t ) x + X ( t , x ) , where A ( t ) is an almost periodic ( n × n ) -matrix and m o d ( A ) m o d ( X ) = { 0 } . We consider the existence problem for almost periodic irregular with respect to m o d ( A ) solutions of such system. This problem is reduced to a similar problem for a system of smaller dimension, and sufficient...