From bimodal one-dimensional maps to Hénon-like two-dimensional maps: does quantitative universality survive?

1994 ◽  
Vol 184 (6) ◽  
pp. 413-421 ◽  
Author(s):  
A.P. Kuznetsov ◽  
S.P. Kuznetsov ◽  
I.R. Sataev
Keyword(s):  
Two Dimensional ◽  
One Dimensional ◽  
One Dimensional Maps

Thermodynamic formalism for certain nonhyperbolic maps

1999 ◽  
Vol 19 (5) ◽  
pp. 1365-1378 ◽  
Author(s):  
MICHIKO YURI
Keyword(s):  
Number Theory ◽  
Gibbs Measure ◽  
Existence And Uniqueness ◽  
Thermodynamic Formalism ◽  
Periodic Points ◽  
Two Dimensional ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Conformal Measures ◽  
One Dimensional Maps

We establish a generalized thermodynamic formalism for certain nonhyperbolic maps with countably many preimages. We study existence and uniqueness of conformal measures and statistical properties of the equilibrium states absolutely continuous with respect to the conformal measures. We will see that such measures are not Gibbs but satisfy a version of Gibbs property (weak Gibbs measure). We apply our results to a one-parameter family of one-dimensional maps and a two-dimensional nonconformal map related to number theory. Both of them admit indifferent periodic points.

FPGA Implementations for Chaotic Maps Using Fixed-Point and Floating-Point Representations

2016 ◽  
pp. 59-97
Author(s):  
Ricardo Francisco Martinez-Gonzalez ◽  
Ruben Vazquez-Medina ◽  
Jose Alejandro Diaz-Mendez ◽  
Juan Lopez-Hernandez
Keyword(s):  
Fixed Point ◽  
Mathematical Description ◽  
Chaotic Maps ◽  
Similarity Coefficient ◽  
Floating Point ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
One Dimensional Maps

This work presents the implementation of various chaotic maps; among the maps there are one-dimensional and two-dimensional ones. In order to implement the maps, their mathematical descriptions are modified to be represented with more accuracy by different binary representations. The sequences from the same map are compared to determine until which iteration, different descriptions produce similar outputs. The similarity coefficient is established in five percent. Comparison delivers some interesting findings; first, the one-dimensional maps, in this work, have comparative number of similar iterations. Second, the bi-dimensional maps present the lowest and highest number of similar iterations. Based on the modified mathematical descriptions, the VHDL implementations are developed. They are simulated and their results are compared against the modified mathematical description ones; resulting that both groups of results are congruent.

ASSOCIATIVE AND RANDOM ACCESS MEMORY USING ONE-DIMENSIONAL MAPS

1992 ◽  
Vol 02 (03) ◽  
pp. 483-504 ◽  
Author(s):  
Yu. V. ANDREYEV ◽  
A. S. DMITRIEV ◽  
L. O. CHUA ◽  
C. W. WU
Keyword(s):  
Random Access ◽  
Random Access Memory ◽  
Two Dimensional ◽  
Access Memory ◽  
One Dimensional ◽  
One Dimensional Maps

A method for storing and retrieving information on the stable cycles of one-dimensional maps as proposed in Dmitriev [1991], Dmitriev, Panas & Starkov [1991] is considered. The applicability of this method in storing and retrieving two-dimensional pictures is demonstrated. Possible extensions by compressing information are discussed. An implementation of random access memory using a one-dimensional map is also considered.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

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