scholarly journals A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity

1988 ◽  
Vol 8 (3) ◽  
pp. 425-435 ◽  
Author(s):  
Tomasz Nowicki
Keyword(s):  
Critical Point ◽  
Critical Value ◽  
Periodic Points ◽  
Hyperbolic Structure ◽  
Liapunov Exponent ◽  
Uniform Hyperbolicity

AbstractA positive Liapunov exponent for the critical value of an S-unimodal mapping implies a positive Liapunov exponent of the backward orbit of the critical point, uniform hyperbolic structure on the set of periodic points and an exponential diminution of the length of the intervals of monotonicity. This is the proof of the Collet-Eckmann conjecture from 1981 in the general case.

scholarly journals Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dipankar Barman ◽  
Subhajit Barman ◽  
Bibhas Ranjan Majhi
Keyword(s):  
Mutual Information ◽  
Critical Point ◽  
Thermal Field ◽  
Narrow Range ◽  
Critical Value ◽  
Critical Values ◽  
Parallel Motion ◽  
Field Temperature ◽  
The Right

Abstract We investigate the effects of field temperature T(f) on the entanglement harvesting between two uniformly accelerated detectors. For their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, T(f) affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors A and B are in the right and left Rindler wedges, respectively. While for T(f) = 0 entanglement harvesting is possible for all values of A’s acceleration aA, in the presence of temperature, it is possible only within a narrow range of aA. In (1 + 1) dimensions, the range starts from specific values and extends to infinity, and as we increase T(f), the minimum required value of aA for entanglement harvesting increases. Moreover, above a critical value aA = ac harvesting increases as we increase T(f), which is just opposite to the accelerations below it. There are several critical values in (1 + 3) dimensions when they are in different accelerations. Contrary to the single range in (1 + 1) dimensions, here harvesting is possible within several discrete ranges of aA. Interestingly, for equal accelerations, one has a single critical point, with nature quite similar to (1 + 1) dimensional results. We also discuss the dependence of mutual information among these detectors on aA and T(f).

scholarly journals Large deviation principles for non-uniformly hyperbolic rational maps

2010 ◽  
Vol 31 (2) ◽  
pp. 321-349 ◽  
Author(s):  
HENRI COMMAN ◽  
JUAN RIVERA-LETELIER
Keyword(s):  
Large Deviation ◽  
Periodic Points ◽  
Rational Maps ◽  
Pressure Function ◽  
Hölder Continuous ◽  
Large Deviation Principles ◽  
Continuous Potential ◽  
Uniform Hyperbolicity ◽  
Level 2 ◽  
Unique Equilibrium State

AbstractWe show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called ‘Topological Collet–Eckmann’. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages. For this purpose we show that each Hölder continuous potential admits a unique equilibrium state, and that the pressure function can be characterized in terms of iterated preimages, periodic points, and Birkhoff averages. Then we use a variant of a general result of Kifer.

THE BAROMETRIC FORMULA FOR REAL GASES AND ITS APPLICATION NEAR THE CRITICAL POINT

1933 ◽  
Vol 9 (6) ◽  
pp. 637-640 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Molecular Weight ◽  
Critical Temperature ◽  
Temperature Gradient ◽  
Critical Point ◽  
Van Der Waals ◽  
Critical Value ◽  
Uniform Density ◽  
Van Der Waals Equation ◽  
Other Substances ◽  
Separation Of Isotopes

According to the theory of the continuity of liquid and gaseous states, as expressed for instance in van der Waals' equation, pronounced density differences may exist in a short column of fluid maintained, throughout its length, at the critical temperature. The point in the tube at which the density of the contents has decreased a given percentage from the critical value is the higher the larger the ratio of the critical temperature to molecular weight. For substances like neon the variations are so large that a measurable separation of isotopes may be expected at or near the critical point; for other substances the computed results are at least of the magnitude found by experiment. Also, according to the theory, in order to obtain, at or near the critical point, a column of gas of uniform density a temperature gradient must be allowed to exist along the column.

Polymerisation processes with intrapolymer bonding. II. Stratified processes

1980 ◽  
Vol 12 (1) ◽  
pp. 116-134 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Critical Point ◽  
Reaction Rates ◽  
Critical Value ◽  
Unstable Stratification ◽  
Local Fluctuations ◽  
Polymer Size ◽  
Spatially Homogeneous ◽  
New Feature ◽  
Size And Structure

We consider a polymerisation process stratified in that space is divided into regions, between which migration occurs, but with bonding occurring only within a region. In the case of a process whose specification is spatially homogeneous, criticality (gelation) is then easily detectable as the point at which statistical equidistribution over regions becomes unstable. Stratification does import a new feature, however, in that the equipartition solution can become metastable below criticality; local fluctuations of density can induce ‘gelational collapse’ at a density below the critical value. We derive also detailed results for the inhomogeneous case, both below and above criticality. Statistics of polymer size and structure are also easily determined in the stratified case, although one can locate the critical point without recourse to these. Finally, one can to a large extent treat the case in which inter- and intrapolymer reaction rates differ, and show that such difference affects the onset of metastability rather than of instability.

scholarly journals Renormalization for Lorenz maps of monotone combinatorial types

2017 ◽  
Vol 39 (1) ◽  
pp. 132-158
Author(s):  
DENIS GAIDASHEV
Keyword(s):  
Critical Point ◽  
A Priori ◽  
Periodic Points ◽  
Unit Interval ◽  
Return Maps ◽  
Lorenz Maps

Lorenz maps are maps of the unit interval with one critical point of order $\unicode[STIX]{x1D70C}>1$ and a discontinuity at that point. They appear as return maps of sections of the geometric Lorenz flow. We construct real a priori bounds for renormalizable Lorenz maps with certain monotone combinatorics and a sufficiently flat critical point, and use these bounds to show existence of periodic points of renormalization, as well as existence of Cantor attractors for dynamics of infinitely renormalizable Lorenz maps.

Homeomorphic restrictions of smooth endomorphisms of an interval

1992 ◽  
Vol 12 (3) ◽  
pp. 429-439 ◽  
Author(s):  
Karen M. Brucks ◽  
Maria Victoria Otero-Espinar ◽  
Charles Tresser
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Periodic Points ◽  
Limit Set ◽  
Asymptotic Dynamics ◽  
Infinite Set

AbstractWe describe the asymptotic dynamics of homeomorphisms obtained as restrictions of generic C2 endomorphisms of an interval with finitely many critical points, all of which are non-flat, and with all periodic points hyperbolic. The ω -limit set of such a restricted endomorphism cannot be infinite, except when the restriction of the endomorphism to the closure of the orbit of some critical point is a minimal homeomorphism of an infinite set.

scholarly journals HUBUNGAN ANTARA NILAI KRITIS DERIVATIF- F^\alpha DENGAN DIMENSI-\gamma DARI SUATU KURVA

2012 ◽  
Vol 4 (1) ◽  
pp. 233
Author(s):  
Supriyadi Wibowo
Keyword(s):  
Critical Point ◽  
Critical Value ◽  
Fractal Set ◽  
Irregular Structure

Continue function that defined on fractal set  is a function which has irregular structure, that can not be an ordinary differentiable on F. In this paper will be explored the correlation between critical point of the derivatif  with dimension-  of a curve. By using the properties of the derivative  , Holder’s continue function in rank of  and dimension , has been obtained the correlation between critical value of derivative and the dimension  of a curve.

Approximate Chiral Symmetry, in Medium Pion Mass, and the PI-Abnormal Nuclear State

1997 ◽  
Vol 06 (02) ◽  
pp. 323-330
Author(s):  
Qi-Ren Zhang ◽  
Walter Greiner
Keyword(s):  
Binding Energy ◽  
Critical Point ◽  
Pion Mass ◽  
Critical Density ◽  
Nuclear Data ◽  
Critical Value ◽  
Nuclear State ◽  
Nuclear Model ◽  
Nuclear Density ◽  
Chiral Angle

In an approximately chiral symmetric nuclear model consistent with the empirical nuclear data, we find that the medium pion mass approaches zero when the nuclear density approaches a critical value. At this critical density a chiral rotation occurs. The binding energy pernucleon jumps from about 16 MeV to 85 MeV. Since the chiral angle is not zero, we call this new state the pi-abnormal nuclear state. In this new state the pion mass becomes about 140 MeV again. Then it decreases with further increase of the nuclear density until it reaches another critical point. At this second point, the chiral angle reaches π. The pion mass starts rising. We identify this phase with the Lee–Wick's abnormal nuclear state.

scholarly journals Shadowing by non-uniformly hyperbolic periodic points and uniform hyperbolicity

Nonlinearity ◽  
2006 ◽  
Vol 20 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Armando Castro ◽  
Krerley Oliveira ◽  
Vilton Pinheiro
Keyword(s):  
Periodic Points ◽  
Uniform Hyperbolicity
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