scholarly journals When is a dynamical system mean sensitive?

2017 ◽  
Vol 39 (06) ◽  
pp. 1608-1636 ◽  
Author(s):  
FELIPE GARCÍA-RAMOS ◽  
JIE LI ◽  
RUIFENG ZHANG
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
The Other ◽  
Positive Entropy ◽  
Topological Dynamical System ◽  
Other Hand ◽  
Open Question ◽  
Uniquely Ergodic ◽  
Mean Sensitivity ◽  
Transitive System

This article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.

scholarly journals Mean equicontinuity and mean sensitivity

2014 ◽  
Vol 35 (8) ◽  
pp. 2587-2612 ◽  
Author(s):  
JIAN LI ◽  
SIMING TU ◽  
XIANGDONG YE
Keyword(s):  
Dynamical System ◽  
Invariant Measure ◽  
Discrete Spectrum ◽  
Stable System ◽  
Positive Entropy ◽  
Zero Entropy ◽  
Open Question ◽  
Mean Sensitivity ◽  
Spectrum Dichotomy

Answering an open question affirmatively it is shown that every ergodic invariant measure of a mean equicontinuous (i.e. mean-L-stable) system has discrete spectrum. Dichotomy results related to mean equicontinuity and mean sensitivity are obtained when a dynamical system is transitive or minimal. Localizing the notion of mean equicontinuity, notions of almost mean equicontinuity and almost Banach mean equicontinuity are introduced. It turns out that a system with the former property may have positive entropy and meanwhile a system with the latter property must have zero entropy.

Generic rotation sets

2020 ◽  
pp. 1-13
Author(s):  
SEBASTIÁN PAVEZ-MOLINA
Keyword(s):  
Dynamical System ◽  
Convex Body ◽  
Probability Measures ◽  
Topological Dynamical System ◽  
Continuous Vector ◽  
Rotation Set ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Uniquely Ergodic ◽  
Dense Set

Abstract Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

Uncertainty Relation: From Inequality to Equality

1997 ◽  
Vol 52 (1-2) ◽  
pp. 49-52 ◽  
Author(s):  
Georg Süssmann
Keyword(s):  
Phase Space ◽  
Quantum State ◽  
Uncertainty Relation ◽  
The Other ◽  
Mixed States ◽  
Von Neumann ◽  
Other Hand ◽  
Pure Quantum State ◽  
Minimum Uncertainty

Abstract The uncertainty area δ (p, q): - [∫ W(p, q)2 dp dq] - 1 is proposed in place of δ p • δ q, and it is shown that each pure quantum state is a minimum uncertainty state in this sense: δ (p, q) = 2 π ħ. For mixed states, on the other hand, δ(p, q) > 2π ħ. In a phase space of 2F(=6N) dimensions, S: = k B • log[δF (p,q)/(2 π ħ)F] whit δF (p,q):= [∫ W(p, q)2 dF p dF q]-1 is considered as an alternative to von Neumann`s entropy S̃:= kB • trc [ρ̂ log (ρ̂-1)].

scholarly journals Egalitarian men: stereotypes and discrimination in the labor market

2020 ◽  
Vol 23 (2) ◽  
pp. 111-147
Author(s):  
Hyalle Abreu Viana ◽  
Ana Raquel Rosas Torres ◽  
José Luis Álvaro Estriamana
Keyword(s):  
Labor Market ◽  
University Students ◽  
Gender Equality ◽  
The Other ◽  
Work Context ◽  
Family Responsibilities ◽  
Men And Women ◽  
Other Hand ◽  
Open Question ◽  
Do So

This article aimed to analyze the stereotypes attributed to "egalitarian men", understood here as men who support gender equality in relation to domestic and family responsibilities as well as inclusion in the workforce. To do so, two studies were carried out. The first study investigated the attribution of stereotypes to egalitarian men through a single open question. A total of 250 university students participated in this study, of which 51.1% were male, and their average age was 21.5 years (SD = 4.39). The second study analyzed the attribution of stereotypes to egalitarian or traditional men and women in a work context considered masculine. Participants included 221 university students with a mean age of 21.9 years (SD = 4.19), the majority (54.3%) being male. Taken together, the results of the two studies indicate that the egalitarian man is perceived as fragile and possibly homosexual. On the other hand, he is also seen as being more competent than traditional men.

Phase Space Reconstruction

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Statistical Mechanics ◽  
State Space ◽  
Phase Plane ◽  
Material Point ◽  
The Other ◽  
Straight Line ◽  
Mathematical Construction

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical construction with important applications in statistical mechanics, to represent the time evolution of a dynamical system in geometric shape. This space has as many dimensions as the number of variables needed to define the instantaneous state of the system. For instance, the state of a material point moving on a straight line is defined by its position and velocity at each instant, so that the phase space for this system is a plane in which one axis is the position and the other one the velocity. In this case, the phase space is also called “phase plane”. It is later applied in many chapters of the book.

scholarly journals V.—What is a Metamorphic Rock?

1911 ◽  
Vol 8 (8) ◽  
pp. 356-361
Author(s):  
E. H. L. Schwarz
Keyword(s):  
Metamorphic Rock ◽  
The Other ◽  
Boric Oxide ◽  
Other Hand ◽  
First Case ◽  
Ore Bodies ◽  
The Masses ◽  
Open Question

The latest book on metamorphism, Dr. V. Grubenmann's Kristallinen Schiefer, still leaves it an open question what a metamorphic rock is. Generally speaking there is no doubt about the matter; every geologist has a more or less precise idea of what he means by the term, but no one has yet been able to propound a definition which is perfectly satisfactory, and which will enable one to distinguish a metamorphic rock from all other kinds and at the same time convey an expression of the characteristic peculiarities inherent in such a rock. The need of a definition is very necessary. The want of it has led Dr. Grubenmann to include some rocks among the crystalline schists which one ordinarily would not refer to that class, and on the other hand there are some rocks frequently referred to that class which are not included. In the first case, the masses of emery form the twelfth group of Dr. Grubenmann's classification, yet the analysis of the Naxos emery, which reveals traces of boric oxide (1.15 per cent. in one case) would seem to place these lenses among the ore-bodies deposited by pneumatolitic action.

Science with the Australia Telescope (Invited Paper)

1987 ◽  
Vol 7 (2) ◽  
pp. 220-226 ◽  
Author(s):  
B. J. Robinson
Keyword(s):  
Phase Space ◽  
Real Time ◽  
The Other ◽  
The Real ◽  
New Science ◽  
Long Baseline ◽  
Other Hand ◽  
Selection Of ◽  
Compact Array

AbstractThe research now under way with the real-time 275 km Parkes-Tidbinbila interferometer is used as a guide to the initial science to be undertaken with the 319 km Australia Telescope (AT) Long Baseline Array. On the other hand, it is risky to guess at the new science likely to be attempted with the 6 km AT Compact Array at Culgoora; instead the potential that has been built into this array is discussed and a selection of basic questions in astrophysics is posed as a guide to significant science that might yield to new observers on a fresh instrument under the southern skies. In conclusion two questions are probed: Can discoveries be made by users of national facilities? Does the AT cross into new domains in the phase space of observations?

scholarly journals Egalitarian men: stereotypes and discrimination in the labor market

2020 ◽  
Vol 23 (2) ◽  
pp. 111-147
Author(s):  
Hyalle Abreu Viana ◽  
Ana Raquel Rosas Torres ◽  
José Luis Álvaro Estriamana
Keyword(s):  
Labor Market ◽  
University Students ◽  
Gender Equality ◽  
The Other ◽  
Work Context ◽  
Family Responsibilities ◽  
Men And Women ◽  
Other Hand ◽  
Open Question ◽  
Do So

This article aimed to analyze the stereotypes attributed to "egalitarian men", understood here as men who support gender equality in relation to domestic and family responsibilities as well as inclusion in the workforce. To do so, two studies were carried out. The first study investigated the attribution of stereotypes to egalitarian men through a single open question. A total of 250 university students participated in this study, of which 51.1% were male, and their average age was 21.5 years (SD = 4.39). The second study analyzed the attribution of stereotypes to egalitarian or traditional men and women in a work context considered masculine. Participants included 221 university students with a mean age of 21.9 years (SD = 4.19), the majority (54.3%) being male. Taken together, the results of the two studies indicate that the egalitarian man is perceived as fragile and possibly homosexual. On the other hand, he is also seen as being more competent than traditional men.

scholarly journals Limit Sets of Weil–Petersson Geodesics

2018 ◽  
Vol 2019 (24) ◽  
pp. 7604-7658
Author(s):  
Jeffrey Brock ◽  
Christopher Leininger ◽  
Babak Modami ◽  
Kasra Rafi
Keyword(s):  
Single Point ◽  
Teichmüller Space ◽  
The Other ◽  
Teichmuller Space ◽  
Limit Set ◽  
Limit Sets ◽  
Other Hand ◽  
Ending Lamination ◽  
Uniquely Ergodic

Abstract In this paper we prove that the limit set of any Weil–Petersson geodesic ray with uniquely ergodic ending lamination is a single point in the Thurston compactification of Teichmüller space. On the other hand, we construct examples of Weil–Petersson geodesics with minimal non-uniquely ergodic ending laminations and limit set a circle in the Thurston compactification.

Can one always lower topological entropy?

1991 ◽  
Vol 11 (3) ◽  
pp. 535-546 ◽  
Author(s):  
M. Shub ◽  
B. Weiss
Keyword(s):  
Topological Entropy ◽  
The Other ◽  
Positive Entropy ◽  
Other Hand ◽  
Topological System

AbstractWe consider the problem of when does a positive entropy topological system have a continuous factor with strictly smaller entropy. In many cases it is shown that such small entropy factors exist. On the other hand, classes of examples are given where differentiable factors must preserve some of the original entropy.

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