Critical itineraries of maps with constant slope and one discontinuity

Michael Barnsley; Wolfgang Steiner; Andrew Vince

doi:10.1017/S0305004114000486

Critical itineraries of maps with constant slope and one discontinuity

Michael Barnsley
, Wolfgang Steiner
, Andrew Vince

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

Original language	English
Pages (from-to)	547-565
Number of pages	19
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	157
Issue number	3
DOIs	https://doi.org/10.1017/S0305004114000486
Publication status	Published - 16 Nov 2014

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title = "Critical itineraries of maps with constant slope and one discontinuity",

abstract = "For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.",

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AU - Barnsley, Michael

AU - Steiner, Wolfgang

AU - Vince, Andrew

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N2 - For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

AB - For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

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DO - 10.1017/S0305004114000486

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JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -

Critical itineraries of maps with constant slope and one discontinuity

Abstract

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