Inverse limits of Markov interval maps

Holte, Sarah

doi:10.1016/s0166-8641(01)00209-7

Cited by 12 publications

(9 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following definition we generalize the notion of Markov interval functions from the case where A is finite to the case where A is countable (including the case when A is countably infinite). One can easily see that every (generalized) Markov interval function (as defined in [3] and [1]) is also a countably Markov interval function. The set A is finite, therefore also countable and the set A ′ in this case is empty.…”

Section: The Straight Line Segment With Endpointsmentioning

confidence: 99%

See 1 more Smart Citation

Inverse limits with countably Markov interval functions

Črepnjak

Lunder

2016

Glas. Mat. Ser. III

View full text Add to dashboard Cite

show abstract

Section: The Straight Line Segment With Endpointsmentioning

confidence: 99%

“…S. Holte proved under which conditions two inverse limits with Markov interval bonding functions are homeomorphic [3]. A generalization of Markov interval maps was introduced in [1], where authors defined so-called generalized Markov interval functions.…”

Section: Introductionmentioning

confidence: 99%

Inverse limits with countably Markov interval functions

Črepnjak

Lunder

2016

Glas. Mat. Ser. III

View full text Add to dashboard Cite

show abstract

“…for examples see [3,4,5,6,7]. In present paper we give sufficient conditions on set-valued functions F and G from a large class of upper semicontinuous functions such that their inverse limits are homeomorphic.…”

Section: Introductionmentioning

confidence: 99%

Δ-related functions and generalized inverse limits

Sovič

2019

Glas. Mat. Ser. III

View full text Add to dashboard Cite

For any continuous single-valued functions f, g : [0, 1] → [0, 1] we define upper semicontinuous set-valued functions F, G : [0, 1] ⊸ [0, 1] by their graphs as the unions of the diagonal ∆ and the graphs of setvalued inverses of f and g respectively. We introduce when two functions are ∆-related and show that if f and g are ∆-related, then the inverse limits lim −⊸ F and lim −⊸ G are homeomorphic. We also give conditions under which lim −⊸ G is a quotient space of lim −⊸ F .

show abstract

“…The inverse limits of Markov interval maps have also been extensively studied. In [6], it is shown that if two Markov interval maps follow the same pattern, then their inverse limits are homeomorphic. This result has been generalized in several ways within the family of set-valued functions (see [2][3][4]).…”

Section: Introductionmentioning

confidence: 99%

Topological entropy of Markov set-valued functions

Alvin¹,

Kelly²

2019

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

We investigate the entropy for a class of upper semi-continuous set-valued functions, called Markov set-valued functions, that are a generalization of single-valued Markov interval functions. It is known that the entropy of a Markov interval function can be found by calculating the entropy of an associated shift of finite type. In this paper, we construct a similar shift of finite type for Markov set-valued functions and use this shift space to find upper and lower bounds on the entropy of the set-valued function.

show abstract

Inverse limits of Markov interval maps

Cited by 12 publications

References 13 publications

Inverse limits with countably Markov interval functions

Inverse limits with countably Markov interval functions

Δ-related functions and generalized inverse limits

Topological entropy of Markov set-valued functions

Contact Info

Product

Resources

About