The Accumulation of Boundary Doubling for Modified Tent Maps

The trajectory of the turning point is dense for almost all tent maps

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700009962 ◽

1996 ◽

Vol 16 (6) ◽

pp. 1173-1183 ◽

Cited By ~ 10

Author(s):

Karen Brucks ◽

Michal Misiurewicz

Keyword(s):

Lebesgue Measure ◽

Turning Point ◽

Tent Map ◽

Tent Maps ◽

Almost All

AbstractWe prove that for almost every (with respect to the Lebesgue measure) a ∈ [√2, 2], the forward trajectory of the turning point of the tent map fa with slope a is dense in the interval of transitivity of fa.

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Inverse Limits on [0,1] Using Tent Maps and Certain Other Piecewise Linear Bonding Maps

Continua ◽

10.1201/9781003072379-19 ◽

2020 ◽

pp. 253-258

Author(s):

W. T. Ingram

Keyword(s):

Piecewise Linear ◽

Inverse Limits ◽

Tent Maps

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Speech encryption using generalized modified chaotic logistic and tent maps

2018 IEEE International Conference on Industrial Technology (ICIT) ◽

10.1109/icit.2018.8352407 ◽

2018 ◽

Cited By ~ 2

Author(s):

Wafaa S. Sayed ◽

Mohammed F. Tolba ◽

Ahmed G. Radwan ◽

Salwa K. Abd-El-Hafiz

Keyword(s):

Tent Maps ◽

Speech Encryption

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Symmetric Tent Maps

Topics from One-Dimensional Dynamics ◽

10.1017/cbo9780511617171.011 ◽

2004 ◽

pp. 147-177

Keyword(s):

Tent Maps

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A current mode analog circuit for tent maps using piecewise linear functions

Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94 ◽

10.1109/iscas.1994.409542 ◽

2002 ◽

Cited By ~ 9

Author(s):

J.T. Bean ◽

P.J. Langlois

Keyword(s):

Analog Circuit ◽

Piecewise Linear ◽

Current Mode ◽

Linear Functions ◽

Piecewise Linear Functions ◽

Tent Maps ◽

A Current

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MULTIFRACTAL MEASURES OF TIME SERIES: f(α) SURFACES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127410027106 ◽

2010 ◽

Vol 20 (08) ◽

pp. 2453-2470

Author(s):

WILLIAM MARTINO ◽

MICHAEL FRAME

Keyword(s):

Time Series ◽

Transition Matrix ◽

Financial Data ◽

Contraction Map ◽

Tent Maps ◽

Data Points ◽

Multifractal Measures

Binning the data points of a time series and associating a contraction map with each bin gives rise to a driven IFS representation of the time series. Varying the bins changes the driven IFS, sometimes in complex ways difficult to parse. From the transition matrix for any particular binning we can plot an f(α) curve. Assembling these curves as the bins change gives a surface, which we call the f(α) surface. We use properties of this surface to investigate time series from iterating logistic and tent maps, and also time series of financial data.

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