scholarly journals Poisson suspensions and infinite ergodic theory

2009 ◽  
Vol 29 (2) ◽  
pp. 667-683 ◽  
Author(s):  
EMMANUEL ROY
Keyword(s):  
Dynamical Systems ◽  
Spectral Theory ◽  
Ergodic Theory ◽  
Mixing Properties ◽  
New Approach ◽  
Infinite Measure ◽  
Infinite Ergodic Theory

AbstractWe investigate the ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure-preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite-measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaussian dynamical systems.

scholarly journals Wheat Grinding Process with Low Moisture Content: A New Approach for Wholemeal Flour Production

Processes ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 32
Author(s):  
Waleed H. Hassoon ◽  
Dariusz Dziki ◽  
Antoni Miś ◽  
Beata Biernacka
Keyword(s):  
Particle Size ◽  
Moisture Content ◽  
Average Particle Size ◽  
Average Particle ◽  
Grinding Process ◽  
Mixing Properties ◽  
New Approach ◽  
Grain Moisture ◽  
Flour Production ◽  
And Storage

The objective of this study was to determine the grinding characteristics of wheat with a low moisture content. Two kinds of wheat—soft spelt wheat and hard Khorasan wheat—were dried at 45 °C to reduce the moisture content from 12% to 5% (wet basis). Air drying at 45 °C and storage in a climatic chamber (45 °C, 10% relative humidity) were the methods used for grain dehydration. The grinding process was carried out using a knife mill. After grinding, the particle size distribution, average particle size and grinding energy indices were determined. In addition, the dough mixing properties of wholemeal flour dough were studied using a farinograph. It was observed that decreasing the moisture content in wheat grains from 12% to 5% made the grinding process more effective. As a result, the average particle size of the ground material was decreased. This effect was found in both soft and hard wheat. Importantly, lowering the grain moisture led to about a twofold decrease in the required grinding energy. Moreover, the flour obtained from the dried grains showed higher water absorption and higher dough stability during mixing. However, the method of grain dehydration had little or no effect on the results of the grinding process or dough properties.

scholarly journals Category Theory for Autonomous and Networked Dynamical Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Ergodic Theory ◽  
Category Theory ◽  
Open Systems ◽  
Topological Dynamics ◽  
Control Problems ◽  
Natural Conditions ◽  
Discussion Paper ◽  
Open Systems Theory

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

FREQUENCY SYNCHRONIZATION IN NETWORKS OF COUPLED OSCILLATORS, A MONOTONE DYNAMICAL SYSTEMS APPROACH

2009 ◽  
Vol 19 (12) ◽  
pp. 4107-4116 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Systems Approach ◽  
System Size ◽  
Coupling Scheme ◽  
Frequency Synchronization ◽  
Nonlinear Coupling ◽  
New Approach ◽  
Monotone Dynamical Systems

We propose a new approach to investigate the frequency synchronization in networks of coupled oscillators. By making use of the theory of monotone dynamical systems, we show that frequency synchronization occurs in networks of coupled oscillators, provided the coupling scheme is symmetric, connected, and strongly cooperative. Our criterion is independent of the system size, the coupling strength and the details of the connections, and applies also to nonlinear coupling schemes.

Infinite ergodic theory for Kleinian groups

2005 ◽  
Vol 25 (4) ◽  
pp. 1305-1323 ◽  
Author(s):  
MANUEL STADLBAUER ◽  
BERND O. STRATMANN
Keyword(s):  
Ergodic Theory ◽  
Kleinian Groups ◽  
Infinite Ergodic Theory

Erratum to ‘Semi-hyperbolic fibered rational maps and rational semigroups’ (Ergodic Theory and Dynamical Systems 26 (2006), 893–922)

2008 ◽  
Vol 28 (3) ◽  
pp. 1043-1045 ◽  
Author(s):  
HIROKI SUMI
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theory ◽  
Rational Maps

AbstractWe give a correction to the assumption of Theorems 1.12 and 2.6 in the paper [H. Sumi. Semi-hyperbolic fibered rational maps and rational semigroups. Ergod. Th. & Dynam. Sys.26 (2006), 893–922].

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