Non-vanishing derivatives of Lyapunov exponents and the pressure function

SHRIHARI SRIDHARAN

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Non-vanishing derivatives of Lyapunov exponents and the pressure function

机译：Lyapunov指数的非零导数与压力函数。

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In this note, we consider the family of hyperbolic quadratic polynomials P{sub}c(z)=z{sup}2+c; c∈[0, 1/4) and discuss its Lyapunov characteristic exponents. We make use of the structural stability of this family and show that the results of Manning on Lyapunov exponents for Julia sets do not generalize to other Bernoulli measures.

机译：在本说明中，我们考虑双曲二次多项式族P {sub} c（z）= z {sup} 2 + c; c∈[0，1/4）并讨论其李雅普诺夫特征指数。我们利用该族的结构稳定性，证明Manning在Julia集的Lyapunov指数上的结果不能推广到其他Bernoulli测度。

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《Dynamical Systems》 |2006年第4期|p.491-500|共10页
作者
SHRIHARI SRIDHARAN;
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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
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正文语种 eng
中图分类工程基础科学;
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7. EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed TarekShahriar Abstract—An EMD-chaos based approach is proposed todiscriminate EEG signals corresponding to healthy persons,and epileptic patients during seizure-free intervals and seizureattacks. An electroencephalogram (EEG) is first empiricallydecomposed to intrinsic mode functions (IMFs). The nonlineardynamics of these IMFs are quantified in terms of the largestLyapunov exponent (LLE) and correlation dimension (CD).This chaotic analysis in EMD domain is applied to a large groupof EEG signals corresponding to healthy persons as well asepileptic patients (both with and without seizure attacks). It isshown that the values of the obtained LLE and CD exhibitfeatures by which EEG for seizure attacks can be clearlydistinguished from other EEG signals in the EMD domain.Thus, the proposed approach may aid researchers in developingeffective techniques to predict seizure activities. Index Terms—Electroencephalogram (EEG), empiricalmode decomposition (EMD), largest Lyapunov exponent (LLE),correlation dimension (CD), epileptic seizures. The Authors are with the Electrical and Electronic EngineeringDepartment, Bangladesh University of Engineering and Technology,Dhaka-1000, Bangladesh (e-mail: imamul@eee.buet.ac.bd) PDF Cite: S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed Tarek Shahriar, "EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain," International Journal of Computer and Electrical Engineering vol. 4, no. 3, pp. 326-330, 2012. PREVIOUS PAPER Perception of Emotions Using Constructive Learningthrough Speech NEXT PAPER Physical Layer Impairments Aware OVPN Connection Selection Mechanisms Copyright © 2008-2013. International Association of Computer Science and Information Technology Press (IACSIT Press) [O] . S. M. Shafiul Alam, Syed TarekShahriar 2012

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Non-vanishing derivatives of Lyapunov exponents and the pressure function

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