Random products of maps synchronizing on average

Matias, Edgar; Melo, Ítalo

doi:10.1142/s021919971950086x

Commun. Contemp. Math.

2020

DOI: 10.1142/s021919971950086x

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Random products of maps synchronizing on average

Edgar Matias

Ítalo Melo

Abstract: We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.

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2023

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“…Note that the definition in[MM20,GK16] differs from the one given here:(F , p, d) is SA if for every x, y ∈ M, for almost every ξ ∈ Σ + N it holds…”

mentioning

confidence: 99%

Contracting on average iterated function systems by metric change

Gelfert,

Salcedo

2023

Nonlinearity

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We study contraction conditions for an iterated function system (IFS) of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space, which turn the IFS into one which is contracting on average. For the particular case of a system of C 1-diffeomorphisms of the circle which is proximal and does not have a probability measure simultaneously invariant by every map, we derive an equivalent metric which contracts on average and conclude that it carries a unique stationary probability measure. Here we strongly use local contraction properties established by Malicet in 2017, which then imply that the IFS has a negative random Lyapunov exponent and generalizes a result by Baxendale.

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“…Note that the definition in[MM20,GK16] differs from the one given here:(F , p, d) is SA if for every x, y ∈ M, for almost every ξ ∈ Σ + N it holds…”

mentioning

confidence: 99%

Contracting on average iterated function systems by metric change

Gelfert,

Salcedo

2023

Nonlinearity

View full text Add to dashboard Cite

show abstract

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Random products of maps synchronizing on average

Abstract: We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.

Cited by 1 publication

References 24 publications

Contracting on average iterated function systems by metric change

Contracting on average iterated function systems by metric change

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