Displaying similar documents to “Inverse limits of tentlike maps on trees”

Structure of inverse limit spaces of tent maps with finite critical orbit

Sonja Štimac (2006)

Fundamenta Mathematicae

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Using methods of symbolic dynamics, we analyze the structure of composants of the inverse limit spaces of tent maps with finite critical orbit. We define certain symmetric arcs called bridges. They are building blocks of composants. Then we show that the folding patterns of bridges are characterized by bridge types and prove that there are finitely many bridge types.

The Gray filtration on phantom maps

Lê Minh Hà, Jeffrey Strom (2001)

Fundamenta Mathematicae

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This paper is a study of the Gray index of phantom maps. We give a new, tower theoretic, definition of the Gray index, which allows us to study the naturality properties of the Gray index in some detail. McGibbon and Roitberg have shown that if f* is surjective on rational cohomology, then the induced map on phantom sets is also surjective. We show that if f* is surjective just in dimension k, then f induces a surjection on a certain subquotient of the phantom set....

Attractors and Inverse Limits.

James Keesling (2008)

RACSAM

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This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.

Turbulent maps and their ω-limit sets

F. Balibrea, C. La Paz (1997)

Annales Polonici Mathematici

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One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.

Shadowing and expansivity in subspaces

Andrew D. Barwell, Chris Good, Piotr Oprocha (2012)

Fundamenta Mathematicae

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We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.

A uniqueness result for an inverse problem

Robert Dalmasso (2004)

Annales Polonici Mathematici

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We establish a uniqueness result for an overdetermined boundary value problem. We also raise a new question.

Triangularization properties of power linear maps and the Structural Conjecture

Michiel de Bondt, Dan Yan (2014)

Annales Polonici Mathematici

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We discuss several additional properties a power linear Keller map may have. The Structural Conjecture of Drużkowski (1983) asserts that certain two such properties are equivalent, but we show that one of them is stronger than the other. We even show that the property of linear triangularizability is strictly in between. Furthermore, we give some positive results for small dimensions and small Jacobian ranks.