Preston Ch. — Iterates Of Piecewise Monotone Mappings On An Interval :: Электронная библиотека попечительского совета мехмата МГУ

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Preston Ch. — Iterates Of Piecewise Monotone Mappings On An Interval

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Название: Iterates Of Piecewise Monotone Mappings On An Interval

Автор: Preston Ch.

Аннотация:

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.

Язык:

Рубрика: Математика/

Серия: Lecture Notes in Mathematics

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1988

Количество страниц: 166

Добавлена в каталог: 12.09.2008

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Предметный указатель

Almost-invariant (set)      15 89
Attracting (periodic point)      10 56
Central cycle      62
Central sink      59
Central turning point      63
Characteristic sequence      24 183
Cocompatible (mapping)      150
Compatible (mapping)      91
Condensation point      89
conjugate      3 34
Convergent (element of $E_{0}(g)$ )      156
CYCLE      6 28
Cycle, central      62
Cycle, essentially transitive      20 161
Cycle, exact      8 33
Cycle, minimal      46
Cycle, proper      6 29
Cycle, semi-exact      8 33
Cycle, topologically transitive      6 29
Elementary (refinement)      21 167 169
End (cycle)      59
Essentially transitive cycle      20 161
Essentially transitive mapping      20 163
Eventual period      109
Eventually periodic component      109
Eventually periodic point      141
Exact cycle      8 33
Exact mapping      7 33
Extension      19 23 148 181
Extension kit      201
Extension sequence      23 182
Extension, primary      20 161
Extension, register-shift      165
Filtration      169
Fixed points      27
Generated (by filtrations)      169
Generator (for a register-shift)      6 30
Homterval      9 54
Invariant (set)      3 89
Iterate      1 26
LAP      26
Mapping, cocompatible      150
Mapping, compatible      91
Mapping, essentially transitive      20 163
Mapping, exact      7 33
Mapping, piecewise monotone      1 26
Mapping, semi-exact      7 33
Mapping, strongly transitive      35
Mapping, uniformly piecewise linear      8 34 73
Maximally (n, $\varepsilon$ )-separated      83

Minimal (cycle)      46
Neighbours      150
Non-elementary (refinement)      21 167
Orbit      1
Perfect (set)      16 89
Period      9 27 28 109
Periodic component      109
Periodic element of $E_{0}(g)$       156
Periodic point      9 27
Periodic point, attracting      10 56
Periodic point, eventually      141
Piecewise monotone (mapping)      1 26
Primary extension      20 161
Primary reduction      17 113 123
Proper (cycle)      6 29
Reduction      13 73 88
Reduction, primary      17 113 123
Reduction, register-shift      121
refinement      20 167 169
Refinement, elementary      21 167 169
Refinement, non-elementary      21 167
Refinement, separated      174
Refinement, transitive      22 169
Register-shift      6 30
Register-shift extension      165
Register-shift reduction      121
Register-shift, tame      11 68 118
Residual (set)      27
Semi-exact cycle      8 33
Semi-exact mapping      7 33
Sensitive dependence to initial conditions      35
Separated ( (n, $\varepsilon$ )-separated )      83
Separated ( (n, $\varepsilon$ )-separated ), maximally      83
Separated cycles      171
Separated hull      172
Separated refinement      174
Sink      9 54
Sink, central      59
Slope (of uniformly piecewice linear mapping)      8 34 73
Splits      49
Splitting (sequence of cycles)      5 30
Strongly transitive (mapping)      35
Supports (a register-shift)      120
Tame (register-shift)      11 68 118
Topologically transitive cycle      6 29
Transitive (refinement)      22 169
Trap      59
Turning point      2 26
Turning point, central      63
Uniformly piecewise linear (mapping)      8 34 73
Weakly-invariant (set)      16 89

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