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- W2035719410 abstract "It follows that (*) has a periodic solution xo(t) such that lim1t1,.*0 e(x(t), x0(t)) = 0 for every solution x(t). Now suppose A(t) is almost periodic. Suppose inf, E(xI(t), x2(t)) = 0 for each pair of solutions xl(t), x2(t) of (*). We look for analogies with the periodic case. For example, let (:, R) be the projective flow (2.3) generated by (*). We ask if (:, R) admits a minimal, almost automorphic subflow (M, R) (2.1; see [13]). Such an M would be an analogue of the periodic solution xo(t) mentioned in the last paragraph. We will show that the answer to this question is no. We will show that there are equations (*) whose projective flow is a miniimal, proximal extension of the hull [11] of A (see 2.1). This means that: (i) inf, e(x1(t), x2(t)) = 0 for all solutions xl(t), x2(t) of (*); (ii) the angular coordinate 0(t) of every solution x(t) of (*) wanders densely through the set of all directions in the sense that, if 00 E [0, 2wT), then there is a sequence t,, oo such that A(t + t) -* A(t) uniformly, and 9(tj) -* 90 mod 27T. We will also find equations (*) such that, in addition to the above, (:, R) is strictly ergodic (2.1). We will use ideas similar to those of Glasner and Weiss [6]. They in turn refer to a paper of Anosov and Katov [1] and Fathi-Herman [4]. We note that Ellis (see [3])" @default.
- W2035719410 created "2016-06-24" @default.
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- W2035719410 date "1981-03-01" @default.
- W2035719410 modified "2023-09-26" @default.
- W2035719410 title "Two-dimensional, almost periodic linear systems with proximal and recurrent behavior" @default.
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- W2035719410 doi "https://doi.org/10.1090/s0002-9939-1981-0612732-9" @default.
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