Chaotic intermittency in maps with infinite derivative

Elaskar, Sergio; Río, Ezequiel del; Lorenzón, Denis

doi:10.1109/argencon49523.2020.9505502

Cited by 1 publication

(7 citation statements)

References 45 publications

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“…We highlight that Equation ( 51) is similar to Equation (21) of Ref. [40]. However, there is a fundamental conceptual difference.…”

Section: First Testmentioning

confidence: 61%

“…where x r is a pre-reinjection point. However, the exponent γ results in γ = 1/j, where j is a positive integer [40]. This paper introduces a theory that generalizes the previous studies obtaining a comprehensive analytical approximation for the RPD function.…”

Section: Introductionmentioning

confidence: 75%

“…Here, we describe two previous studies to calculate the exponent γ [39,40]. In Section 3, we show that both works are only particular cases of the theory introduced in this paper.…”

Section: The Rpd Functionmentioning

confidence: 94%

“…A method to calculate the exponents γ and α for maps with derivatives lim x→x r dF(x) dx → ∞ has been presented in a recent paper [40]. This paper only studies maps like Equation (7) shows.…”

Section: Map Derivative Tends To Infinity At Pre-reinjection Pointsmentioning

confidence: 99%

“…We highlight that, to use this framework, F(x) must be injective around x r [44]. Also, this scheme applies to maps y = F(x) for which there are no analytical inverse functions [40]. However, γ is restricted to rational numbers 1/j, where j is an integer number.…”

Section: Map Derivative Tends To Infinity At Pre-reinjection Pointsmentioning

confidence: 99%

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Theoretical Evaluation of the Reinjection Probability Density Function in Chaotic Intermittency

Elaskar

Río

2023

Symmetry

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The traditional theory of chaotic intermittency developed for return maps hypothesizes a uniform density of reinjected points from the chaotic zone to the laminar one. In the past few years, we have described how the reinjection probability density function (RPD) can be generalized as a power law function. Here, we introduce a broad and general analytical approach to determine the RPD function and other statistical variables, such as the characteristic relation traditionally utilized to characterize the chaotic intermittency type. The proposed theoretical methodology is simple to implement and includes previous studies as particular cases. It is compared with numerical data, the M function methodology, and the Perron–Frobenius technique, showing high accuracy between them.

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“…We highlight that Equation ( 51) is similar to Equation (21) of Ref. [40]. However, there is a fundamental conceptual difference.…”

Section: First Testmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 75%

“…Here, we describe two previous studies to calculate the exponent γ [39,40]. In Section 3, we show that both works are only particular cases of the theory introduced in this paper.…”

Section: The Rpd Functionmentioning

confidence: 94%

Section: Map Derivative Tends To Infinity At Pre-reinjection Pointsmentioning

confidence: 99%

Section: Map Derivative Tends To Infinity At Pre-reinjection Pointsmentioning

confidence: 99%

See 3 more Smart Citations

Theoretical Evaluation of the Reinjection Probability Density Function in Chaotic Intermittency

Elaskar

Río

2023

Symmetry

Self Cite

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show abstract

Chaotic intermittency in maps with infinite derivative

Cited by 1 publication

References 45 publications

Theoretical Evaluation of the Reinjection Probability Density Function in Chaotic Intermittency

Theoretical Evaluation of the Reinjection Probability Density Function in Chaotic Intermittency

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