Inverse limits with countably Markov interval functions

Črepnjak, Matevž; Lunder, Tjaša

doi:10.3336/gm.51.2.14

Cited by 12 publications

(7 citation statements)

References 5 publications

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“…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

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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 .

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Section: Introductionmentioning

confidence: 99%

Δ-related functions and generalized inverse limits

Sovič

2019

Glas. Mat. Ser. III

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“…In this context, one may associate to any Markov multi-map of the interval a shift of finite type (SFT) that captures the combinatorics of the multi-map. Markov multi-maps have been studied in recent years with a focus on how the associated SFT can be used to investigate the topological structure of the inverse limit [2,5,6,11], as well as its topological entropy [3,18].…”

Section: Introductionmentioning

confidence: 99%

Topological dynamics of Markov multi-maps of the interval

Kelly¹,

McGoff²

2021

Preprint

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We study Markov multi-maps of the interval from the point of view of topological dynamics. Specifically, we investigate whether they have various properties, including topological transitivity, topological mixing, dense periodic points, and specification. To each Markov multi-map, we associate a shift of finite type (SFT), and then our main results relate the properties of the SFT with those of the Markov multi-map. These results complement existing work showing a relationship between the topological entropy of a Markov multi-map and its associated SFT. We also characterize when the inverse limit systems associated to the Markov multi-maps have the properties mentioned above.

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“…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]). In this paper, we focus on Markov set-valued functions as defined in [2] and investigate the topological entropy of such maps.…”

Section: Introductionmentioning

confidence: 99%

Topological entropy of Markov set-valued functions

Alvin¹,

Kelly²

2019

Ergod. Th. Dynam. Sys.

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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.

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Inverse limits with countably Markov interval functions

Cited by 12 publications

References 5 publications

Δ-related functions and generalized inverse limits

Δ-related functions and generalized inverse limits

Topological dynamics of Markov multi-maps of the interval

Topological entropy of Markov set-valued functions

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