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Iterated nonlinear maps and Hilbert’s projective metric. II. (English) Zbl 0669.47031
Mem. Am. Math. Soc. 401, 118 p. (1989).
From author’s abstract: If $$u\in\overset\circ K$$ is an eigenvector of $$f$$ of norm one and if $$g(x) = f(x)\| f(x)\|^{-1}$$, is it true that $$\lim_{k\to\infty} g^ k (x) = u$$ for every $$x \in \overset\circ K$$?
If f has no eigenvector in $$\overset\circ K$$, what can be said about the behavior of $$f^ k(x)$$ or $$g^ k(x)$$ for $$k\geq1$$ and $$x\in \overset\circ K$$?
After an introduction and preliminaries, the chapters deal with applications to some examples from mathematical biology, eigenvectors for $$f\in M_-$$ and D-A-D theorems.
[For part I see ibid. 391, 137 p. (1988; Zbl 0666.47028); for a preliminary version see also NATO ASI Ser., Ser. F 37, 231-248 (1987; Zbl 0643.47050).]
Reviewer: D.Pascali

##### MSC:
 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 47H10 Fixed-point theorems 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems 47B60 Linear operators on ordered spaces 92D25 Population dynamics (general)
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