We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the wellknown notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (chain recurrence and chain mixing times). We give upper and lower bounds for these recurrence times and relate the chain mixing time to topological entropy.
We introduce topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that are expansive and have the shadowing property) on noncompact and non-metrizable spaces that generalize theorems for such homeomorphisms on compact metric spaces. The main result is a generalization of Smale's spectral decomposition theorem to topologically Anosov homeomorphisms on first countable locally compact paracompact Hausdorff spaces.
The influence of different dietary factors on the quality and safety of rabbit meat is discussed in this chapter. The nutritive value of rabbit meat is presented as well as its sensory properties and processing characteristics. Emphasis is given on the effects of dietary energy, feed restriction, dietary fibre, dietary protein, dietary fat and antioxidants on the quality of rabbit meat.
We show that a continuous map or a continuous flow on R n with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in R n intersects W then there is a fixed point in W . Consequently, if the omega limit set of every point is nonempty and uniformly bounded then there is a fixed point.
Fathi and Pageault have recently shown a connection between Auslander's
generalized recurrent set $GR(f)$ and Easton's strong chain recurrent set. We
study $GR(f)$ by examining that connection in more detail, as well as
connections with other notions of recurrence. We give equivalent definitions
that do not refer to a metric. In particular, we show that $GR(f^k)=GR(f)$ for
any $k>0$, and give a characterization of maps for which the generalized
recurrent set is different from the ordinary chain recurrent set.Comment: Revised version incorporates referee's comment
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