Periodic orbits of maps of y

Llufs AlsedÀ; Jaume Llibre; Michal Misiurewicz

doi:10.1090/S0002-9947-1989-0958882-0

Periodic orbits of maps of y

Llufs AlsedÀ, Jaume Llibre, Michal Misiurewicz

Department of Mathematics

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

49 Citations (Scopus)

Abstract

We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z ∈ C: z3 ∈ [0, 1]) into itself having zero as a fixed point. We also obtain new proofs of some known results for maps of an interval into itself. © 1989 American Mathematical Society.

Original language	English
Pages (from-to)	475-538
Journal	Transactions of the American Mathematical Society
Volume	313
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1989-0958882-0
Publication status	Published - 1 Jan 1989

Keywords

Periodic orbit
Primary orbit
Set of periods
Šarkovskii theorem

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abstract = "We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z ∈ C: z3 ∈ [0, 1]) into itself having zero as a fixed point. We also obtain new proofs of some known results for maps of an interval into itself. {\textcopyright} 1989 American Mathematical Society.",

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N2 - We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z ∈ C: z3 ∈ [0, 1]) into itself having zero as a fixed point. We also obtain new proofs of some known results for maps of an interval into itself. © 1989 American Mathematical Society.

AB - We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z ∈ C: z3 ∈ [0, 1]) into itself having zero as a fixed point. We also obtain new proofs of some known results for maps of an interval into itself. © 1989 American Mathematical Society.

KW - Periodic orbit

KW - Primary orbit

KW - Set of periods

KW - Šarkovskii theorem

U2 - 10.1090/S0002-9947-1989-0958882-0

DO - 10.1090/S0002-9947-1989-0958882-0

M3 - Article

VL - 313

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EP - 538

IS - 2

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