By Munkres J.R.
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16, 345– 354 (1983) 48. : The linked twist map approach to fluid mixing, Dynamical Systems and Statistical Mechanics, London Mathematical Society Durham Symposium 2006. dur. html 49. : The topology of stirred fluids. Topology Appl. 1. To put the emphasis on the sets K j s, we may also say that ψ induces chaotic dynamics on two symbols on the set D with respect to K0 and K1 . This definition corresponds to the concept of chaos in the coin-tossing sense stated in . However, the definition in  is enhanced here with the condition on periodic sequences.
2 17, 277–364 (1961) 5. : On the relations among various entropy characteristics of dynamical systems. Izv. Akad. Nauk SSSR Ser. Mat. 35, 324–366 (1971) 6. : A geometric criterion for positive topological entropy. Comm. Math. Phys. 172, 95–118 (1995) 7. : Introduction to the modern theory of dynamical systems. With a supplementary chapter by Katok and Leonardo Mendoza. Encyclopedia of Mathematics and its Applications, vol. 54. Cambridge University Press, Cambridge (1995) 8. : A simple guide to chaos and complexity.
1). Given a generalized rectangle R and S := [0, 1]2 ⊆ R2 the associated homeomorphism h : S → h(S ) = R, the set ϑ R := h(∂([0, 1]2 )), where ∂([0, 1]2 ) is the usual boundary of the unit square, is named the contour of R. the contour ϑ R is well-defined as it is independent of the choice of the homeomorphism h. In fact, ϑ R is also a homeomorphic image of a simple closed curve, that is, a Jordan curve. We also call as an oriented rectangle, the pair R := (R, R − ) where R ⊆ X is a generalized rectangle and R − := Rl− ∪ Rr− is the union of two disjoint compact arcs Rl− and Rr− ⊆ ϑR that we call the left and right sides of R − .
Analysis of manifolds by Munkres J.R.