Sinks, sources and saddles for expansive flows with the pseudo-orbits tracing property
The simplest shadowing
Two different and easy proofs are presented that a hyperbolic linear homeomorphism of a Banach space admits the shadowing.
Saddles for expansive flows with the pseudo orbits tracing property
Let F be an expansive flow with the pseudo orbits tracing property on a compact metric space X. Suppose X is connected, locally connected and contains at least two distinct orbits. Then any point is a saddle.
Shadowing for linear systems of differential equations.
For a system of linear ordinary differential equations with constant coefficients a simple proof is given that hyperbolicity is equivalent to shadowing.
On the placement of applied mathematics
I was asked by Professor Vladimir Zwonka an opinion in connection with the ongoing discussion in the Committee of Mathematical Sciences of the place of applied mathematics. After sending him to my preliminary remarks, I decided to expand the text a little more and deliver it to Lords honorable professors also. My speech gonna put me finish a practical, it seems to me, proposition.
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