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Full-Text Articles in Mathematics
Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram
Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram
Mathematics and Statistics Faculty Research & Creative Works
In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from a two-parameter family of piecewise linear unimodal bonding maps. This investigation focuses on the parameter values at the boundary between a hereditarily decomposable inverse limit and an inverse limit containing an indecomposable continuum. © 1999 American Mathematical Society.
Inverse Limits On [0,1] Using Logistic Bonding Maps, Marcy Barge, William Thomas Ingram
Inverse Limits On [0,1] Using Logistic Bonding Maps, Marcy Barge, William Thomas Ingram
Mathematics and Statistics Faculty Research & Creative Works
In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from the logistic family, fλ (x) = 4λx(1-x) for 0 ≤ λ ≤ 1. Many interesting continua occur as such inverse limits from arcs to indecomposable continua. Among other things we observe that up through the Feigenbaum limit the inverse limit is a point or is hereditarily decomposable and otherwise the inverse limit contains an indecomposable continuum. © 1996 Elsevier Science B.V. All rights reserved.
Periodicity And Indecomposability, William Thomas Ingram
Periodicity And Indecomposability, William Thomas Ingram
Mathematics and Statistics Faculty Research & Creative Works
In this paper we characterize the existence of periodic points of odd period greater than one for unimodal mappings of an interval onto itself. The interesting juxtaposition of this condition with the occurrence in inverse limits of the well-known Brouwer-Janiszewski-Knaster continuum is explored. Also obtained is a characterization of indecomposability of certain inverse limits using a single unimodal bonding map. © 1995 American Mathematical Society.
Periodic Points For Homeomorphisms Of Hereditarily Decomposable Chainable Continua, W. T. Ingram
Periodic Points For Homeomorphisms Of Hereditarily Decomposable Chainable Continua, W. T. Ingram
Mathematics and Statistics Faculty Research & Creative Works
In this paper it is shown that homeomorphisms of hereditarily decomposable chainable continua cannot have periodic points whose periods are not powers of two. Examples show that for each power of two there is a hereditarily decomposable chainable continuum and a homeomorphism of it which has a periodic point of period that power of two. © 1989 American Mathematical Society.
Concerning Periodic Points In Mappings Of Continua, W. (William) T. (Thomas) Ingram
Concerning Periodic Points In Mappings Of Continua, W. (William) T. (Thomas) Ingram
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present some conditions which are sufficient for a mapping to have periodic points. © 1988 American Mathematical Society.