scholarly journals Complex dynamics with focus on the real part

2015 ◽  
Vol 37 (1) ◽  
pp. 176-192 ◽  
Author(s):  
JOHN ERIK FORNÆSS ◽  
HAN PETERS
Keyword(s):  
Complex Dynamics ◽  
The Real ◽  
Ergodic Properties

We consider the dynamics of holomorphic polynomials in$\mathbb{C}$. We show that the ergodic properties of the map can be seen already from the real parts of the orbits.

A reconstruction theorem for complex polynomials

2015 ◽  
Vol 26 (09) ◽  
pp. 1550073 ◽  
Author(s):  
Luka Boc Thaler
Keyword(s):  
Real Axis ◽  
Ergodic Theory ◽  
Complex Dynamics ◽  
Julia Set ◽  
Complex Polynomials ◽  
Analogous Statement ◽  
The Real ◽  
Ergodic Properties ◽  
Reconstruction Theorem ◽  
Exceptional Polynomials

Recently Takens' Reconstruction Theorem was studied in the complex analytic setting by Fornæss and Peters [Complex dynamics with focus on the real part, to appear in Ergodic Theory Dynam. Syst.]. They studied the real orbits of complex polynomials, and proved that for non-exceptional polynomials ergodic properties such as measure theoretic entropy are carried over to the real orbits mapping. Here we show that the result from [Complex dynamics with focus on the real part, to appear in Ergodic Theory Dynam. Syst.] also holds for exceptional polynomials, unless the Julia set is entirely contained in an invariant vertical line, in which case the entropy is 0. In [The reconstruction theorem for endomorphisms, Bull. Braz. Math. Soc. (N.S.) 33(2) (2002) 231–262.] Takens proved a reconstruction theorem for endomorphisms. In this case the reconstruction map is not necessarily an embedding, but the information of the reconstruction map is sufficient to recover the (2m + 1) th image of the original map. Our main result shows an analogous statement for the iteration of generic complex polynomials and the projection onto the real axis.

scholarly journals Research on the Complex Dynamic Characteristics and RLS Estimation’s Influence Based on Price and Service Game

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Zhanbing Guo
Keyword(s):  
Least Squares ◽  
Fixed Points ◽  
Dynamic Characteristics ◽  
Complex Dynamics ◽  
Recursive Least Squares ◽  
Game Model ◽  
Complex Dynamic ◽  
Service Market ◽  
The Real ◽  
Price Game

Considering that the real competitions in service market contain two important factors, price and service, we build a dynamical price and service game model and study the complex dynamics of this bivariate game. Some special properties about the adjustment of service are noted by comparing our innovative bivariate game model with previous univariate game model. Besides, we discuss the stabilities of fixed points and compare the price and service game with price game. What is more, the recursive least-squares (RLS) estimation is introduced to substitute naive estimation; then the impacts of RLS estimation are studied by comparing it with naive estimation.

scholarly journals Equidistribution problems in complex dynamics of higher dimension

2017 ◽  
Vol 28 (07) ◽  
pp. 1750057 ◽  
Author(s):  
Tien-Cuong Dinh ◽  
Nessim Sibony
Keyword(s):  
Dynamical System ◽  
Complex Dynamics ◽  
Fundamental Problem ◽  
Arbitrary Dimension ◽  
Deep Understanding ◽  
Periodic Points ◽  
Higher Dimension ◽  
Open Problems ◽  
New Techniques ◽  
Ergodic Properties

Equidistribution of the orbits of points, subvarieties or of periodic points in complex dynamics is a fundamental problem. It is often related to strong ergodic properties of the dynamical system and to a deep understanding of analytic cycles, or more generally positive closed currents, of arbitrary dimension and degree. The later topic includes the study of the potentials and super-potentials of positive closed currents, their intersection with or without dimension excess. In this paper, we will survey some results and tools developed during the last two decades. Related concepts, new techniques and open problems will be presented.

scholarly journals Rich dynamics of a Filippov avian-only influenza model with a nonsmooth separation line

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Youping Yang ◽  
Jingwen Wang
Keyword(s):  
Complex Dynamics ◽  
Sliding Mode ◽  
Dynamical Behavior ◽  
Threshold Level ◽  
Control Measures ◽  
Sliding Modes ◽  
Threshold Policy ◽  
Effective Measure ◽  
The Real ◽  
Separation Line

AbstractDepopulation of birds has been authenticated to be an effective measure in controlling avian influenza transmission. In this work, we establish a Filippov avian-only model incorporating a threshold policy control. We choose the index—the maximum between the infected threshold level $I_{T}$ I T and the product of the number of susceptible birds S and a ratio threshold value ξ—to decide on whether to trigger the control measures or not, which then leads to a discontinuous separation line and two pieces of sliding-mode domains. Meanwhile, one more sliding-mode domain gives birth to more complex dynamics. We investigate the global dynamical behavior of the Filippov model, including the real and/or virtual equilibria and the two sliding modes and their dynamics. The solutions will eventually stabilize at the real endemic equilibrium of the subsystem or the pseudoequilibria on the two sliding modes due to different threshold values. Therefore an effective and efficient threshold policy is essential to control the influenza by driving the number of infected birds below a certain level or at a previously given level.

Robust Performance Analysis of Uncertain Magnetic Bearings

2000 ◽  
Author(s):  
Toru Namerikawa ◽  
Masayuki Fujita
Keyword(s):  
Performance Analysis ◽  
Closed Loop ◽  
Complex Dynamics ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Design Model ◽  
Robust Performance ◽  
The Real ◽  
And Performance ◽  
Interconnection Structure

This paper deals with uncertain model structures, model validation and robust performance analysis of active magnetic bearing systems. The dynamics of active magnetic bearing systems are characterized by their instability and complex dynamics of rotor and electromagnets. One of the most critical problems of AMBs is a description of a complex behavior of the dynamics of electromagnets and their forces. The exact description of them is almost hopeless, some approximations and assumptions must be employed, and consequently a discrepancy between the real physical system and the nominal design model cannot be avoided. This discrepancy of the magnetic bearing systems is a serious problem of stability and performance. Hence feedback control is indispensable to stabilize the system, further the closed-loop systems of AMBs should have robustness for stability and performance against model uncertainties. First we derive a nominal mathematical model of AMBs as a linear state-space model under some assumption and idealization, then we consider the discrepancy between the real physical systems and the obtained nominal design model. This discrepancy can be expressed as the structured uncertainties by Linear Fractional Transformation. These uncertainties include linearization error, parametric uncertainties, unmodeled dynamics, and gyroscopic effect. Then we set the interconnection structure which contains the above structurally represented uncertainties. Next we design a robust controller which achieves robust performance condition. Finally, we validate the interconnection structure with the nominal model and uncertainties, and analyze the robustness of stability and performance of the closed-loop system via the mixed structured singular value.

Time Optimal Compressor Valve Soft Landing by Two Step ILC

2011 ◽  
Author(s):  
Hannes Trogmann ◽  
Harald Waschl ◽  
Daniel Alberer ◽  
Bernhard Spiegl
Keyword(s):  
Iterative Learning Control ◽  
Complex Dynamics ◽  
High Energy ◽  
Soft Landing ◽  
Valve Design ◽  
Constrained Optimal Control ◽  
The Real ◽  
Time Optimal ◽  
Active Valve ◽  
High Energy Consumption

Normally compressor load control is realized either passively with a bypass loop with high energy consumption or by an active valve. Actively controlled valves must fulfill a set of conditions which can be expressed as a constrained optimal control. However, compressor valves are subject to serious disturbances which might be unpredictable and difficult to describe, and have complex dynamics. This makes the solution of the real optimal problem difficult and even questionable. Against this background, this paper proposes a two step design approach: first a problem approximation is derived for which an explicit solution of the problem can be computed, then iterative learning control (ILC) is used with the real plant to enforce it. Due to limitation of the actuators, basically a switching solution results, and the tracking of this solution yields a satisfactory solution near to the optimal one. The method has been tested in simulation and experimentally on a special valve design including a small rotational electrical motor and a high gear rate spindle.

Scanning electron microscopy of human iliac bone by a simple preparation method

1990 ◽  
Vol 48 (3) ◽  
pp. 226-227
Author(s):  
Toshihiko Takita ◽  
Tomonori Naguro ◽  
Toshio Kameie ◽  
Akihiro Iino ◽  
Kichizo Yamamoto
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Preparation Method ◽  
Specimen Preparation ◽  
Real Surface ◽  
Public Attention ◽  
Preparation Methods ◽  
The Real ◽  
Simple Preparation ◽  
Scanning Electron

Recently with the increase in advanced age population, the osteoporosis becomes the object of public attention in the field of orthopedics. The surface topography of the bone by scanning electron microscopy (SEM) is one of the most useful means to study the bone metabolism, that is considered to make clear the mechanism of the osteoporosis. Until today many specimen preparation methods for SEM have been reported. They are roughly classified into two; the anorganic preparation and the simple preparation. The former is suitable for observing mineralization, but has the demerit that the real surface of the bone can not be observed and, moreover, the samples prepared by this method are extremely fragile especially in the case of osteoporosis. On the other hand, the latter has the merit that the real information of the bone surface can be obtained, though it is difficult to recognize the functional situation of the bone.

Personal Audio System: Hearing Symptoms, Habits, and Sound Pressure Levels Measured in Real Ear and a Manikin

2020 ◽  
Vol 63 (6) ◽  
pp. 2016-2026
Author(s):  
Tamara R. Almeida ◽  
Clayton H. Rocha ◽  
Camila M. Rabelo ◽  
Raquel F. Gomes ◽  
Ivone F. Neves-Lobo ◽  
...  
Keyword(s):  
Sound Pressure ◽  
Daily Basis ◽  
Cross Sectional Study ◽  
Normal Hearing ◽  
Chi Square ◽  
Cross Sectional ◽  
The Real ◽  
Significant Difference ◽  
Sound Pressure Levels ◽  
Audio System

Purpose The aims of this study were to characterize hearing symptoms, habits, and sound pressure levels (SPLs) of personal audio system (PAS) used by young adults; estimate the risk of developing hearing loss and assess whether instructions given to users led to behavioral changes; and propose recommendations for PAS users. Method A cross-sectional study was performed in 50 subjects with normal hearing. Procedures included questionnaire and measurement of PAS SPLs (real ear and manikin) through the users' own headphones and devices while they listened to four songs. After 1 year, 30 subjects answered questions about their usage habits. For the statistical analysis, one-way analysis of variance, Tukey's post hoc test, Lin and Spearman coefficients, the chi-square test, and logistic regression were used. Results Most subjects listened to music every day, usually in noisy environments. Sixty percent of the subjects reported hearing symptoms after using a PAS. Substantial variability in the equivalent music listening level (Leq) was noted ( M = 84.7 dBA; min = 65.1 dBA, max = 97.5 dBA). A significant difference was found only in the 4-kHz band when comparing the real-ear and manikin techniques. Based on the Leq, 38% of the individuals exceeded the maximum daily time allowance. Comparison of the subjects according to the maximum allowed daily exposure time revealed a higher number of hearing complaints from people with greater exposure. After 1 year, 43% of the subjects reduced their usage time, and 70% reduced the volume. A volume not exceeding 80% was recommended, and at this volume, the maximum usage time should be 160 min. Conclusions The habit of listening to music at high intensities on a daily basis seems to cause hearing symptoms, even in individuals with normal hearing. The real-ear and manikin techniques produced similar results. Providing instructions on this topic combined with measuring PAS SPLs may be an appropriate strategy for raising the awareness of people who are at risk. Supplemental Material https://doi.org/10.23641/asha.12431435

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