Asymptotic Periodicity of the Iterates of Positivity Preserving Operators

Miklavcic, M.

doi:10.2307/2001184

Cited by 4 publications

(3 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should also be noted that the space L 1 plays an important role. Results analogous to those of Theorem 1 in other Banach spaces require, in general, much more restrictive assumptions (Miklav6i6 1988, Sine 1989). For example, Y must be strongly compact and 0 = 0.…”

Section: Markov Operatorsmentioning

confidence: 83%

The statistical dynamics of recurrent biological events

1992

View full text Add to dashboard Cite

In this paper we develop a general modeling framework within which many models for systems which produce events at irregular times through a combination of probabilistic and deterministic dynamics can be comprehended. We state and prove new sufficient conditions for the global asymptotic behaviour of the density evolution in these systems, and apply our results to many previously published models for the cell division cycle. In addition, we develop a new interpretation for the statistics of action potential production in excitable cells.

show abstract

Section: Markov Operatorsmentioning

confidence: 83%

The statistical dynamics of recurrent biological events

1992

View full text Add to dashboard Cite

show abstract

“…This result was subsequently extended on L p (μ) spaces, general Banach lattices and recently on ordered Banach spaces with bases (cf. [1,5,20,22]). We do not aim to dive into abstract regions but focus on classical spaces X = L 1 (μ).…”

Section: Preliminaries and Notationmentioning

confidence: 99%

“…Finishing this section it is perhaps worth to mention that besides Lasota's seminal papers [16,17] on constrictivity, essential contribution to this topic was added by Komornik, Li, Yorke, Sine, Emel'yanov, Wolff, Miklavčič and Bartoszek (cf. [1,2,5,7,[11][12][13][14]17,20,22]).…”

Section: Introductionmentioning

confidence: 99%

On asymptotic periodicity of kernel double Markovian operators

Bartoszek

Krzemiński

2020

Positivity

View full text Add to dashboard Cite

show abstract

Riesz decomposition property implies asymptotic periodicity of positive and constrictive operators

Bartoszek¹

1992

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract.Consider a linear and positive operator T acting on an ordered, F-normed linear space X. Assume that there exists an open neighborhood U 3 0 such that the trajectory {T"(x)} is attracted to a compact set Fu whenever x is taken from U and that the positive cone X+ is closed, proper, and reproducing. It is shown that if (X, X+) has the Riesz Decomposition Property then T has asymptotically periodic iterates.

show abstract

Asymptotic Periodicity of the Iterates of Positivity Preserving Operators

Cited by 4 publications

References 6 publications

The statistical dynamics of recurrent biological events

The statistical dynamics of recurrent biological events

On asymptotic periodicity of kernel double Markovian operators

Riesz decomposition property implies asymptotic periodicity of positive and constrictive operators

Contact Info

Product

Resources

About