Uncertainty relation for chaos

Asher Yahalom; Meir Lewkowicz; Jacob Levitan; Gil Elgressy; Lawrence Horwitz; Yossi Ben-Zion

doi:https://doi.org/10.1142/S0219887815500930

Uncertainty relation for chaos

Asher Yahalom, Meir Lewkowicz, Jacob Levitan, Gil Elgressy, Lawrence Horwitz, Yossi Ben-Zion

Ariel University, Tel Aviv University, Bar-Ilan University

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

Abstract

A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times, the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples. We stress that the criterion suggested involves only local exponents and is not concerned with asymptotic defined exponents.

Original language	English
Article number	1550093
Journal	International Journal of Geometric Methods in Modern Physics
Volume	12
Issue number	9
DOIs	https://doi.org/10.1142/S0219887815500930
State	Published - 1 Oct 2015

Keywords

Chaos
geometrical analysis
local exponent

All Science Journal Classification (ASJC) codes

Physics and Astronomy (miscellaneous)

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https://doi.org/10.1142/S0219887815500930

Cite this

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title = "Uncertainty relation for chaos",

abstract = "A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times, the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples. We stress that the criterion suggested involves only local exponents and is not concerned with asymptotic defined exponents.",

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T1 - Uncertainty relation for chaos

AU - Yahalom, Asher

AU - Lewkowicz, Meir

AU - Levitan, Jacob

AU - Elgressy, Gil

AU - Horwitz, Lawrence

AU - Ben-Zion, Yossi

PY - 2015/10/1

Y1 - 2015/10/1

N2 - A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times, the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples. We stress that the criterion suggested involves only local exponents and is not concerned with asymptotic defined exponents.

AB - A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times, the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples. We stress that the criterion suggested involves only local exponents and is not concerned with asymptotic defined exponents.

KW - Chaos

KW - geometrical analysis

KW - local exponent

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DO - https://doi.org/10.1142/S0219887815500930

M3 - مقالة

SN - 0219-8878

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JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

IS - 9

M1 - 1550093

ER -

Uncertainty relation for chaos

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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