PIECEWISE LINEAR MODEL FOR TREE MAPS

2001 ◽  
Vol 11 (12) ◽  
pp. 3163-3169 ◽  
Author(s):  
MATHIEU BAILLIF ◽  
ANDRÉ DE CARVALHO
Keyword(s):  
Linear Model ◽  
Piecewise Linear ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Piecewise Monotone ◽  
Monotone Map ◽  
Piecewise Linear Model ◽  
Constant Slope

We generalize to tree maps the theorems of Parry and Milnor–Thurston about the semi-conjugacy of a continuous piecewise monotone map f to a continuous piecewise linear map with constant slope, equal to the exponential of the entropy of f.

scholarly journals Isomorphisms between positive and negative -transformations

2012 ◽  
Vol 34 (1) ◽  
pp. 153-170 ◽  
Author(s):  
CHARLENE KALLE
Keyword(s):  
Piecewise Linear ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Constant Slope

AbstractWe compare a piecewise linear map with constant slope $\beta \gt 1$ and a piecewise linear map with constant slope $-\beta $. These maps are called the positive and negative $\beta $-transformations. We show that for a certain set of $\beta $s, the multinacci numbers, there exists a measurable isomorphism between these two maps. We further show that for all other values of $\beta $between 1 and 2 the two maps cannot be isomorphic.

One-Dimensional Semiconjugacy Revisited

2003 ◽  
Vol 13 (07) ◽  
pp. 1657-1663 ◽  
Author(s):  
J. F. Alves ◽  
J. Sousa Ramos
Keyword(s):  
Topological Entropy ◽  
Piecewise Linear ◽  
Linear Map ◽  
One Dimensional ◽  
Piecewise Linear Map ◽  
Piecewise Monotone ◽  
Positive Topological Entropy ◽  
Interval Map

Let f be a piecewise monotone interval map with positive topological entropy h(f)= log (s). Milnor and Thurston showed that f is topological semiconjugated to a piecewise linear map having slope s. Here we prove that these semiconjugacies are the eigenvectors of a certain linear endomorphism associated to f. Using this characterization, we prove a conjecture presented by those authors.

Topological conjugation of Lorenz maps by β-transformations

1990 ◽  
Vol 107 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul Glendinning
Keyword(s):  
Topological Entropy ◽  
Piecewise Linear ◽  
Sufficient Conditions ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Necessary And Sufficient ◽  
Constant Slope ◽  
Lorenz Maps ◽  
Basic Sets ◽  
Topological Conjugation

AbstractNecessary and sufficient conditions for a Lorenz map to be topologically conjugate to a piecewise linear map with constant slope (a β-transformation) are given, first in terms of kneading invariants of the maps and then in terms of the topological entropy restricted to basic sets. The dynamics of β-transformations is also described.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

scholarly journals Piecewise linear model of self-organized hierarchy formation

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
Tomoshige Miyaguchi ◽  
Takamasa Miki ◽  
Ryota Hamada
Keyword(s):  
Linear Model ◽  
Piecewise Linear ◽  
Self Organized ◽  
Piecewise Linear Model ◽  
Hierarchy Formation

scholarly journals Effect of Mean Stress on the Fatigue Life Prediction of Notched Fiber-Reinforced 2060 Al-Li Alloy Laminates under Spectrum Loading

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Weiying Meng ◽  
Liyang Xie ◽  
Yu Zhang ◽  
Yawen Wang ◽  
Xiaofang Sun ◽  
...  
Keyword(s):  
Fatigue Life ◽  
Linear Model ◽  
Life Prediction ◽  
Piecewise Linear ◽  
Forecast Accuracy ◽  
Cyclic Stress ◽  
Fatigue Life Prediction ◽  
Fiber Reinforced ◽  
Piecewise Linear Model ◽  
Spectrum Loading

This paper presents a study on the fatigue life prediction of notched fiber-reinforced 2060 Al-Li alloy laminates under spectrum loading by applying the constant life diagram. Firstly, a review on the state of the art of constant life diagram models for the life prediction of composite materials is given, which highlights the effect on the forecast accuracy. Then, the fatigue life of notched fiber-reinforced Al-Li alloy laminates (2/1 laminates and 3/2 laminates) is tested under cyclic stress, which has different stress cycle characteristics (constant amplitude loading and Mini-Twist spectrum loading). The introduced models are successfully realized based on the available experimental data of examined laminates. In the case of Mini-Twist spectrum loading, the effect of the constant life diagram on the life prediction accuracy of examined laminates is studied based on the rainflow-counting method and Miner damage criteria. The results show that the simple Goodman model and piecewise linear model have certain advantages compared to other complex models for the life prediction of notched fiber metal laminates with different structures under Mini-Twist loading. From the engineering perspective, the S-N curve prediction based on the piecewise linear model is most applicable and accurate among all the models.

scholarly journals The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions

2015 ◽  
Vol 25 (13) ◽  
pp. 1550184 ◽  
Author(s):  
Carlos Lopesino ◽  
Francisco Balibrea-Iniesta ◽  
Stephen Wiggins ◽  
Ana M. Mancho
Keyword(s):  
Piecewise Linear ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
The Third ◽  
Autonomous Version ◽  
Area Preserving ◽  
Chaotic Saddle

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous version and we prove that the first and the third Conley–Moser conditions are satisfied, which imply the existence of a chaotic saddle. Finally, we numerically demonstrate how the structure of this nonautonomous chaotic saddle varies as parameters are varied.

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