Measurable time-restricted sensitivity

Domenico Aiello; Hansheng Diao; Zhou Fan; Daniel O. King; Jessica Lin; Cesar E. Silva

doi:10.1088/0951-7715/25/12/3313

Measurable time-restricted sensitivity

Domenico Aiello, Hansheng Diao, Zhou Fan, Daniel O. King, Jessica Lin, Cesar E. Silva

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We develop two notions of sensitivity to initial conditions for measurable dynamical systems, where the time before divergence of a pair of paths is at most an asymptotically logarithmic function of a measure of their initial distance. In the context of probability measure-preserving transformations on a compact space, we relate these notions to the metric entropy of the system. We examine one of these notions for classes of non-measure-preserving, nonsingular transformations.

Original language	English (US)
Pages (from-to)	3313-3325
Number of pages	13
Journal	Nonlinearity
Volume	25
Issue number	12
DOIs	https://doi.org/10.1088/0951-7715/25/12/3313
State	Published - Dec 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

Access to Document

10.1088/0951-7715/25/12/3313

Cite this

@article{3de50ba595374a8899e735287474863e,

title = "Measurable time-restricted sensitivity",

abstract = "We develop two notions of sensitivity to initial conditions for measurable dynamical systems, where the time before divergence of a pair of paths is at most an asymptotically logarithmic function of a measure of their initial distance. In the context of probability measure-preserving transformations on a compact space, we relate these notions to the metric entropy of the system. We examine one of these notions for classes of non-measure-preserving, nonsingular transformations.",

author = "Domenico Aiello and Hansheng Diao and Zhou Fan and King, {Daniel O.} and Jessica Lin and Silva, {Cesar E.}",

year = "2012",

month = dec,

doi = "10.1088/0951-7715/25/12/3313",

language = "English (US)",

volume = "25",

pages = "3313--3325",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "12",

}

TY - JOUR

T1 - Measurable time-restricted sensitivity

AU - Aiello, Domenico

AU - Diao, Hansheng

AU - Fan, Zhou

AU - King, Daniel O.

AU - Lin, Jessica

AU - Silva, Cesar E.

PY - 2012/12

Y1 - 2012/12

N2 - We develop two notions of sensitivity to initial conditions for measurable dynamical systems, where the time before divergence of a pair of paths is at most an asymptotically logarithmic function of a measure of their initial distance. In the context of probability measure-preserving transformations on a compact space, we relate these notions to the metric entropy of the system. We examine one of these notions for classes of non-measure-preserving, nonsingular transformations.

AB - We develop two notions of sensitivity to initial conditions for measurable dynamical systems, where the time before divergence of a pair of paths is at most an asymptotically logarithmic function of a measure of their initial distance. In the context of probability measure-preserving transformations on a compact space, we relate these notions to the metric entropy of the system. We examine one of these notions for classes of non-measure-preserving, nonsingular transformations.

UR - http://www.scopus.com/inward/record.url?scp=84869109968&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869109968&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/25/12/3313

DO - 10.1088/0951-7715/25/12/3313

M3 - Article

AN - SCOPUS:84869109968

SN - 0951-7715

VL - 25

SP - 3313

EP - 3325

JO - Nonlinearity

JF - Nonlinearity

IS - 12

ER -

Measurable time-restricted sensitivity

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this