scholarly journals Hyperbolicity versus weak periodic orbits inside homoclinic classes

2017 ◽  
Vol 38 (6) ◽  
pp. 2345-2400 ◽  
Author(s):  
XIAODONG WANG
Keyword(s):  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Homoclinic Class ◽  
Intrinsic Nature ◽  
Significant Difference ◽  
Stability Conjecture ◽  
The Stability ◽  
Classical Proof ◽  
Homoclinic Classes

We prove that, for$C^{1}$-generic diffeomorphisms, if the periodic orbits contained in a homoclinic class$H(p)$have all their Lyapunov exponents bounded away from zero, then$H(p)$must be (uniformly) hyperbolic. This is in the spirit of the works on the stability conjecture, but with a significant difference that the homoclinic class$H(p)$is not known isolated in advance, hence the ‘weak’ periodic orbits created by perturbations near the homoclinic class have to be guaranteed strictly inside the homoclinic class. In this sense the problem is of an ‘intrinsic’ nature, and the classical proof of the stability conjecture does not work. In particular, we construct in the proof several perturbations which are not simple applications of the connecting lemmas.

scholarly journals Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes

2009 ◽  
Vol 29 (5) ◽  
pp. 1479-1513 ◽  
Author(s):  
LORENZO J. DÍAZ ◽  
ANTON GORODETSKI
Keyword(s):  
Lyapunov Exponents ◽  
Residual Subset ◽  
Homoclinic Class ◽  
Zero Measure ◽  
Ergodic Measures ◽  
Homoclinic Classes

AbstractWe prove that there is a residual subset 𝒮 in Diff1(M) such that, for everyf∈𝒮, any homoclinic class offcontaining saddles of different indices (dimension of the unstable bundle) contains also an uncountable support of an invariant ergodic non-hyperbolic (one of the Lyapunov exponents is equal to zero) measure off.

Stability and mutual impact of perception of parental pressure and infants' social support – A study based on the difference between employment status and household income

2021 ◽  
pp. 002072092199705
Author(s):  
Yong Wang
Keyword(s):  
Household Income ◽  
Employment Status ◽  
Working Mothers ◽  
Social Research ◽  
Research Report ◽  
Parental Pressure ◽  
Income Levels ◽  
Significant Difference ◽  
The Difference ◽  
The Stability

The purpose of this study is to explore the stability and interaction between parental pressure and social research report, as well as the role of employment status and family income levels in this process. This study used a special study on Korean children (PSKC) 2–4 waves. Use t-test, correlation and autoregressive cross-delay modeling to analyze the data. The main findings of this study are: First, over time, parental pressure and mother’s social research report are consistent. Secondly, the pressure of motherhood and childcare has an obvious lagging effect on upbringing, and vice versa. Third, there is no significant difference between working mothers and non-working mothers in terms of the stability of working parents' pressure, social research report and social research report for children's pressure channels. However, parental pressure can only predict the social research report of working mothers. Fourth, there is no significant difference between the stability and interaction of these two structures in household income levels. In short, the results show that, over time, parental pressure is consistent with mother’s social research report. The results also show that there is a significant cross-lag effect between the mothers’ perceptions of mutual pressure analysis. In the process from parental pressure to social research report, I found the difference between working and non-working mothers. The advantage of this study is that the expected longitudinal design was adopted during infancy and the priority between the two structures can be considered. The results of this study can be used as a source of intervention plans to help parents withstand severe parenting pressure and lack of social research report.

On the integrability of intermediate distributions for Anosov diffeomorphisms

1995 ◽  
Vol 15 (2) ◽  
pp. 317-331 ◽  
Author(s):  
M. Jiang ◽  
Ya B. Pesin ◽  
R. de la Llave
Keyword(s):  
Finite Number ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphism ◽  
Anosov Diffeomorphisms ◽  
Stable Foliation

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

The stability analysis using Lyapunov exponents for high-DOF nonlinear vehicle plane motion

2021 ◽  
pp. 095440702110433
Author(s):  
Shuming Shi ◽  
Fanyu Meng ◽  
Minghui Bai ◽  
Nan Lin
Keyword(s):  
Stability Analysis ◽  
Quantitative Analysis ◽  
Lyapunov Exponents ◽  
Plane Motion ◽  
Vehicle Model ◽  
Motion Stability ◽  
Motion System ◽  
Nonlinear Vehicle Model ◽  
The Stability ◽  
Different Characteristics

The Lyapunov exponents method is an excellent approach for analyzing the vehicle plane motion stability, and the researchers demonstrated the effectiveness under 2-DOF vehicle model. However, whether the Lyapunov exponents approach can effectively reveal the characteristics of high-DOF nonlinear vehicle model is the key problem at present. In this paper, the Lyapunov exponents is applied to quantitatively analyze the stability of the nonlinear three and five degree of freedom vehicle plane motion system. The different characteristics between 2-DOF and high-DOF model are revealed and explained by using Lyapunov exponents. It illustrates the feasibility of using Lyapunov exponents to analyze the stability of high-DOF vehicle models, which supplements and perfects the existing quantitative analysis conclusion.

scholarly journals Efficacy of Selective Grinding Guided by an Occlusal Splint in Management of Myofascial Pain: A Prospective Clinical Trial

2017 ◽  
Vol 11 (1) ◽  
pp. 301-311
Author(s):  
Felipe J. Fernández-González ◽  
Jorge Cabero-López ◽  
Aritza Brizuela ◽  
Ivan Suazo ◽  
Esteban Pérez-Pevida ◽  
...  
Keyword(s):  
Temporomandibular Joint ◽  
Myofascial Pain ◽  
Vertical Displacement ◽  
Occlusal Splint ◽  
Significant Difference ◽  
Before And After ◽  
Skeletal Pattern ◽  
Condylar Position ◽  
The Stability ◽  
Facial Types

Background:For patients whose centric relation (CR) has not been considered at the start and during treatment, the task of achieving an occlusal scheme that works together with the temporomandibular joint, the muscles, and the structures of the stomatognathic apparatus becomes a major concern.Objective:This study aims to describe a reproducible, predictable and to date unreported procedure of selective grinding guided by an occlusal splint and to analyze condylar position (CP) based on the skeletal pattern.Methods:A total of 72 symptomatic patients (38 females and 34 males) were classified into three groups: hyperdivergent, intermediate and hypodivergent. CP was quantified by mounted casts on a measures condyle displacement (MCD) device. Helkimo index was also performed in order to assess the severity of the temporomandibular joint (TMJ) disorders attending to clinical dysfunction, occlusal state and anamnestic dysfunction. Once the stability had been obtained, the splint was progressively reduced until the maximum intercuspation (MIC) was achieved.Results:The vertical displacement was found to be significantly different between the hyperdivergent and other two groups (p<0.01). Comparisons of MCD analysis before and after the selective grinding procedure identified a statistically significant difference in the horizontal and vertical CP (p<0.01) between the different groups whereas the Helkimo Index showed a clear improvement of TMJ disorders.Conclusion:All facial types, specially the hyperdivergent face type, showed a reduction in condylar displacement (CD) and less craniomandibular symptoms using this procedure, making it an excellent technique for clinicians.

scholarly journals Radiographic evaluation of the use of transverse traction device in vertebral arthrodesis for degenerative diseases

2014 ◽  
Vol 13 (1) ◽  
pp. 27-30
Author(s):  
Edgar Takao Utino ◽  
João Paulo Machado Bergamaschi ◽  
Luciano Antonio Nassar Pellegrino ◽  
Ricardo Shigueaki Galhego Umeta ◽  
Maria Fernanda Silber Caffaro ◽  
...  
Keyword(s):  
Evaluation Studies ◽  
Fusion Rate ◽  
Radiographic Evaluation ◽  
Pedicle Fixation ◽  
Degenerative Lumbar Diseases ◽  
Significant Difference ◽  
Traction Device ◽  
Consolidation Rate ◽  
The Stability

OBJECTIVE: Perform radiographic analysis of the use of Transverse Traction Device (DTT) with respect to fusion rate in patients submitted to vertebral arthrodesis for degenerative lumbar diseases. METHODS: We selected x-ray images on anteroposterior, lateral and oblique views and with maximum flexion and extension dynamics of 23 patients submitted to posterolateral arthrodesis of the lumbar spine with a minimum follow-up period of six months. The images were evaluated and classified by the Linovitz's system by two spine surgeons. RESULTS: We evaluated the radiographs of 23 patients after the minimum postoperative period of 6 months and of these, 11 have used DTT. With regard to the consolidation rate, seven patients (63.6%) in the group of DTT were classified as fusion as well as six patients (50%) who were not submitted to the treatment. There was no statistical difference between the groups regarding the consolidation rate. CONCLUSION: The use of transverse traction device in this study showed no significant difference in the rate of consolidation in radiographic evaluation. Studies on the effective participation of this device in the stability of pedicle fixation systems are still lacking in the literature.

scholarly journals Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chunru Li ◽  
Zujun Ma
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Media Coverage ◽  
New Product ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Significant Difference ◽  
Form Theory ◽  
The Difference ◽  
The Stability

In this paper, a mathematical model with time-delay-related parameters and media coverage to describe the diffusion process of new products is proposed, in which the time-delay-related parameters denote the stage in which potential customers decide whether to adopt a new product. Then, the stability and the Hopf bifurcation of the proposed model are analyzed in detail. The center manifold theorem and the normal form theory are used to investigate the stability of the bifurcating periodic solution. Moreover, a numerical simulation is conducted to investigate the difference between the model with delay-dependent parameters and that with delay-independent parameters. The results show that there is significant difference between the two models.

scholarly journals The assessment of the stability of the corneal structure after LASIK correction of myopia by different optical zone diameters

2016 ◽  
Vol 73 (6) ◽  
pp. 572-576 ◽  
Author(s):  
Milorad Milivojevic ◽  
Vladimir Petrovic ◽  
Miroslav Vukosavljevic ◽  
Ivan Marjanovic ◽  
Mirko Resan
Keyword(s):  
Structural Parameters ◽  
Preoperative Assessment ◽  
Laser In Situ Keratomileusis ◽  
Group I ◽  
Significant Difference ◽  
Optical Zone ◽  
Corneal Structure ◽  
The Stability ◽  
Corneal Thinning

Background/Aim. Enlargement of optical zone (OZ) diameter during laser in situ keratomileusis (LASIK) correction of myopia postoperatively improves the optical outcome, however, it also leads to the increased stroma tissue consumption - progressive corneal thinning. The aim of this investigation was to present the possibility of safe OZ enlargement without impairing the structural stability of the cornea, while obtaining an improved optical outcome with LASIK treatment of shortsightedness. Methods. Preoperative assessment of the cornea structure and prediction of the ablated stroma tissue consumption was conducted in 37 patients (74 eyes) treated for shortsightedness by means of the LASIK method. With the eyes that, according to their cornea structure, had the capacity for OZ diameter enlargement of 0.5 mm, LASIK treatment was performed within the wider OZ diameter of 7.0 mm compared to the standard 6.5 mm. The following two groups were formed, depending on the diameter of the utilized OZ: the group I (the eyes treated with the OZ 6.5 mm, n = 37) and the group II (the eyes treated with the OZ 7.0 mm, n = 37). Results. No significant difference in the observed structural parameters of the cornea was detected between the groups of patients treated with different OZ diameters. The values of all the parameters were significantly bellow the threshold values for the development of postoperative ectasia. Conclusion. Diameter enlargement of the treated OZ, if there is a preoperative cornea capacity for such enlargement, will not impair the postoperative stability of the cornea structure, and will significantly improve the optical outcome.

Sign in / Sign up

Export Citation Format

Share Document