scholarly journals On piecewise affine interval maps with countably many laps

2011 ◽  
Vol 31 (3) ◽  
pp. 753-762 ◽  
Author(s):  
Jozef Bobok ◽  
◽  
Martin Soukenka
Keyword(s):  
Interval Maps ◽  
Piecewise Affine

scholarly journals Complexity of injective piecewise contracting interval maps

2018 ◽  
Vol 40 (1) ◽  
pp. 64-88 ◽  
Author(s):  
E. CATSIGERAS ◽  
P. GUIRAUD ◽  
A. MEYRONEINC
Keyword(s):  
Growth Rate ◽  
Cantor Set ◽  
Interval Maps ◽  
Piecewise Affine ◽  
Complexity Function ◽  
Asymptotic Dynamics

We study the complexity of the itineraries of injective piecewise contracting maps on the interval. We prove that for any such map the complexity function of any itinerary is eventually affine. We also prove that the growth rate of the complexity is bounded from above by the number, $N-1$, of discontinuities of the map. To show that this bound is optimal, we construct piecewise affine contracting maps whose itineraries all have the complexity $(N-1)n+1$. In these examples, the asymptotic dynamics take place in a minimal Cantor set containing all the discontinuities.

scholarly journals Embedded PWM Predictive Control of Dc-Dc Power Converters via Piecewise-Affine Neural Networks

2021 ◽  
pp. 1-1
Author(s):  
Emilio Tanowe Maddalena ◽  
Martin W. F. Specq ◽  
Viviane Louzada Wisniewski ◽  
Colin Neil Jones
Keyword(s):  
Neural Networks ◽  
Predictive Control ◽  
Power Converters ◽  
Piecewise Affine ◽  
Dc Power
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