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The classification of topologically expansive lorenz maps
Author(s) -
Hubbard John H.,
Sparrow Colin T.
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430402
Subject(s) - expansive , mathematics , classification of discontinuities , topological conjugacy , invariant (physics) , simple (philosophy) , lorenz system , extension (predicate logic) , conjugacy class , pure mathematics , interval (graph theory) , mathematical analysis , combinatorics , attractor , computer science , mathematical physics , physics , philosophy , compressive strength , epistemology , thermodynamics , programming language
We show that topologically expansive Lorenz maps can be described up to topological conjugacy by their kneading invariants. We also give a simple condition on pairs of symbol sequences which is satisfied if and only if that pair of sequences is the kneading invariant for some topologically expansive Lorenz map. A simple extension of the theorems to the case of expansive maps of the interval with multiple discontinuities is described.