Dimension estimate of almost periodic attractors by simultaneous diophantine approximation

[摘要] There Exists In this paper we estimate fractal dimensions of almost periodic trajectories for a semilinear parabolic partial differential equation: partial derivative u/partial derivative t - d(t) Delta u + g(t) u There Exists f(t), where we assume periodicity: d(t + alpha(1)) = d(t), g(t + alpha(2)) = g(t) for irrational numbers alpha(1), alpha(2), which are linearly independent over the rationals, and f(t + 1) = f(t). By using simultaneous Diophantine approximation, we can show that the dimension of the almost periodic attractor is majorized by 1/gamma(1) + 2/gamma(2), where gamma(1) is the minimum number of the exponents of Holder's conditions on the periodic functions and gamma(2) is the secondary minimum. (C) 1997 Academic Press.

[发布日期] 1997-11-20