| Popis: |
We construct a delay functional d U with values in ( 0 , r ) and find a positive number h r such that the negative feedback equation x ′ ( t ) = − x ( t − d U ( x t , r ) ) , with the segment x t , r : [ − r , 0 ] → R given by x t , r ( s ) = x ( t + s ) , has a solution whose short segments x t , h = x t , r | [ − h , 0 ] are dense in an open subset of the space C 1 ( [ − h , 0 ] , R ) . The domain U of d U is open in C 1 ( [ − r , 0 ] , R ) , and the delay differential equation defines a continuous semiflow of continuously differentiable solution operators on the solution manifold { ϕ ∈ U : ϕ ′ ( 0 ) = − ϕ ( − d U ( ϕ ) ) } . The result implies a kind of chaotic solution behaviour which is not confined to a thin Cantor dust. |
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