|
Chaos occupies an important position in the field of power systems, today's hot topics, chaos theory more widely used in almost all fields of science. Been engaged in mathematics, theoretical physics, astronomy and biology workers general concern. research this article has carry to attract sub mapping binary attract the relationship between the sub and its topological entropy. Definition 1 For a manifold M, the map f: M? → M continuous if M closed invariant subset A absorption M of almost all points (Lebesgue measure of the sense), then known as A is f is a attract sub. Moreover, if the restriction mapping f | A topology total yoke in a binary system, then known as A f, one into the bit to attract sub If f | A topology conjugated in a N? binary systems, then A is a 'f N? binary attractor. Let X be a compact system, such as an α, β represents the open cover of the X's. Vocabulary α ∨ β = {A ∩ B | ∈ α A, B ∈ β}, F? (α) = {F? (A) | A ∈ α} Vocabulary 1 1 N (α) for the α sub coverage cardinality lower supremum and wrote H (α) = log N (α) of Definition 2 h (f, α) = lim1H (∨ ni f (α)) ≥ 0?? 1 n → ∞ n = 0 called f relative in open covering α topology entropy. definition of h (f) = sup {h (f, α)} ≥ 0 α 1 lt; WP = 35 gt; summary called topological entropy of f, which sup open covering of X take the supremum topological entropy is an α non-negative real number, but can achieve positive infinity, we can be found in many papers map attractor carry interval [1, 3,5? 9,12]. These mappings have zero topological entropy and they possess attract sub are 2? binary. based on the previous ideas, it is natural to be asked: Are there a the same time has a binary attract sub and positive topological entropy of the mapping? whether the presence of a attractor 2? binary (for example, n = 3) mapping? binary attract What is the relationship between the sub and topological entropy? Through this demonstration, we can see a complex (positive entropy) power system very simple, you can have the power traits the attractor (binary attractor)., the main results of this paper are as follows: 1. defined in the unit closed interval I = [0,1] on the continuous self-mapping f if it has a n? carry attract sub, and n is not a power of 2, then h (f) the gt; 0. 2 by a counter example illustrate the above proposition the inverse proposition is not established. namely: existence of a closed interval [0, 1] carry attractor of continuous self-mapping, it has positive entropy, and if n is not a power of 2, the attractor is not n? carry. 3. discussed the existence of a class of 3rd order Feigenbaum map, and prove that such third-order Feigenbaum map with exactly 3? binary attractor.
|