Acknowledgements

Pinheiro, Marília P. Futre

doi:10.1515/9781501503986-030

Cited by 1 publication

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“…Moreover, f | U is continuous and non-singular. Hence, it follows from Proposition 3.8 of [Pi21] that…”

Section: Baire Ergodicitymentioning

confidence: 92%

“…for every open set (with respect to the induced topology) A and B ⊂ U . A it was proved in [Pi21], in most case, asymptotically transitive is equivalent to be Baire ergodic.…”

Section: Baire Ergodicitymentioning

confidence: 97%

“…It was introduced in [Pi21] the concept of Baire Ergodicity for general Baire topological spaces. In our context, if…”

Section: Baire Ergodicitymentioning

confidence: 99%

“…Proposition 3.1 (See Proposition 4.2 and 4.7 at [Pi21]). If U ⊂ X is a Baire ergodic component of f , then there exists a unique topological attractor A and a unique statistical attractor A * for U .…”

Section: Baire Ergodicitymentioning

confidence: 99%

“…A direct consequence of Theorem B of [Pi21], Lemma 4.10 above and the fact that the periodic points are dense in any cycle of intervals for a continuous map f is a formula for calculating the (upper) Birkhoff average for continuous function along the orbit of generic points in a cycle of intervals.…”

Section: Wandering Intervals and Attractorsmentioning

confidence: 99%

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Topological and statistical attractors for interval maps

Pinheiro¹

2021

Preprint

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We use the concept of Baire Ergodicity and Ergodic Formalism introduced in [Pi21] to study topological and statistical attractors for interval maps, even with discontinuities. For that we also analyze the wandering intervals attractors. As a result, we establish the finiteness of the non-periodic topological attractors for piecewise C 2 maps with discontinuities. For C 2 interval maps without discontinuities, we show the coincidence of the statistical attractors with the topological ones and we calculate the upper Birkhoff averages of continuous functions for generic points, even when the map has abundance of historical behavior.

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“…Moreover, f | U is continuous and non-singular. Hence, it follows from Proposition 3.8 of [Pi21] that…”

Section: Baire Ergodicitymentioning

confidence: 92%

“…for every open set (with respect to the induced topology) A and B ⊂ U . A it was proved in [Pi21], in most case, asymptotically transitive is equivalent to be Baire ergodic.…”

Section: Baire Ergodicitymentioning

confidence: 97%

“…It was introduced in [Pi21] the concept of Baire Ergodicity for general Baire topological spaces. In our context, if…”

Section: Baire Ergodicitymentioning

confidence: 99%

Section: Baire Ergodicitymentioning

confidence: 99%

Section: Wandering Intervals and Attractorsmentioning

confidence: 99%

See 3 more Smart Citations