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1

Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two

100%

Ingram W. T., Roe R.

Colloquium Mathematicum

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1999

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tom 81

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nr 1

51-61

EN

We derive several properties of unimodal maps having only periodic points whose period is a power of 2. We then consider inverse limits on intervals using a single strongly unimodal bonding map having periodic points whose only periods are all the powers of 2. One such mapping is the logistic map, $f_λ(x)$ = 4λx(1-x) on [f(λ),λ], at the Feigenbaum limit, λ ≈ 0.89249. It is known that this map produces an hereditarily decomposable inverse limit with only three topologically different subcontinua. Other examples of such maps are given and it is shown that any two strongly unimodal maps with periodic point whose only periods are all the powers of 2 produce homeomorphic inverse limits whenever each map has the additional property that the critical point lies in the closure of the orbit of the right endpoint of the interval.

2

An atriodic tree-like continuum with positive span which admits a monotone mapping to a chainable continuum

100%

Davis J. F., Ingram W. T.

Fundamenta Mathematicae

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1988

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tom 131

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nr 1

13-24

3

An uncountable collection of mutually exclusive planar atriodic tree-like continua with positive span

99%

Ingram W. T.

Fundamenta Mathematicae

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1974

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tom 85

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nr 1

73-78

4

An atriodic tree-like continuum with positive span

60%

Ingram W. T.

Fundamenta Mathematicae

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1972-1973

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tom 77

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nr 2

99-107

5

Hereditarily indecomposable tree-like continua, II

60%

Ingram W. T.

Fundamenta Mathematicae

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1981

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tom 111

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nr 2

95-106

6

Hereditarily indecomposable tree-like continua

60%

Ingram W. T.

Fundamenta Mathematicae

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1979

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tom 103

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nr 1

61-64

7

Concerning atriodic tree-like continua

50%

Ingram W. T.

Fundamenta Mathematicae

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1978

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tom 101

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nr 3

189-193

Ograniczanie wyników

6 Fundamenta Mathematicae

1 Colloquium Mathematicum

7 Ingram W. T.

1 Davis J. F.

1 Roe R.

1 1999

1 1988

1 1981

1 1979

1 1978

1 1974

1 1972

Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two

An atriodic tree-like continuum with positive span which admits a monotone mapping to a chainable continuum

An uncountable collection of mutually exclusive planar atriodic tree-like continua with positive span

An atriodic tree-like continuum with positive span

Hereditarily indecomposable tree-like continua, II

Hereditarily indecomposable tree-like continua

Concerning atriodic tree-like continua