Iterates of Piecewise Monotone Mappings on an Interval
Preston, Chris.
Iterates of Piecewise Monotone Mappings on an Interval [electronic resource] / by Chris Preston. - VIII, 172 p. online resource. - Lecture Notes in Mathematics, 1347 0075-8434 ; . - Lecture Notes in Mathematics, 1347 .
Piecewise monotone mappings -- Proof of Theorems 2.4 and 2.5 -- Sinks and homtervals -- Examples of register-shifts -- A proof of Parry's theoren (Theorem 2.6) -- Reductions -- The structure of the set D(f) -- Countable closed invariant sets -- Extensions -- Refinements -- Mappings with one turning point -- Some miscellaneous results from real analysis.
Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.
9783540459712
10.1007/BFb0079769 doi
Mathematics.
Real Functions.
QA331.5
515.8
Iterates of Piecewise Monotone Mappings on an Interval [electronic resource] / by Chris Preston. - VIII, 172 p. online resource. - Lecture Notes in Mathematics, 1347 0075-8434 ; . - Lecture Notes in Mathematics, 1347 .
Piecewise monotone mappings -- Proof of Theorems 2.4 and 2.5 -- Sinks and homtervals -- Examples of register-shifts -- A proof of Parry's theoren (Theorem 2.6) -- Reductions -- The structure of the set D(f) -- Countable closed invariant sets -- Extensions -- Refinements -- Mappings with one turning point -- Some miscellaneous results from real analysis.
Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.
9783540459712
10.1007/BFb0079769 doi
Mathematics.
Real Functions.
QA331.5
515.8