scholarly journals One-dimensional and two-dimensional dynamics of cubic maps

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Djellit Ilhem ◽  
Kara Amel
Keyword(s):  
Large Class ◽  
System Parameter ◽  
Two Dimensional ◽  
One Dimensional ◽  
Henon Maps ◽  
Hénon Maps ◽  
Starting Point ◽  
Good Starting Point ◽  
Polynomial Diffeomorphisms

We concentrate on the dynamics of one-dimensional and two-dimensional cubic maps, it describes how complex behaviors can possibly arise as a system parameter changes. This is a large class of diffeomorphisms which provide a good starting point for understanding polynomial diffeomorphisms with constant Jacobian and equivalent to a composition of generalized Hénon maps. Due to the theoretical and practical difficulties involved in the study, computers will presumably play a role in such efforts.

scholarly journals Kneading sequences for toy models of Hénon maps

2020 ◽  
pp. 1-20
Author(s):  
ERMERSON ARAUJO
Keyword(s):  
Conjugacy Class ◽  
Topological Conjugacy ◽  
Two Dimensional ◽  
One Dimensional ◽  
Henon Maps ◽  
Hénon Maps ◽  
Critical Lines ◽  
Model Family

Abstract The purpose of this article is to study the relation between combinatorial equivalence and topological conjugacy, specifically how a certain type of combinatorial equivalence implies topological conjugacy. We introduce the concept of kneading sequences for a setting that is more general than one-dimensional dynamics: for the two-dimensional toy model family of Hénon maps introduced by Benedicks and Carleson, we define kneading sequences for their critical lines, and prove that these sequences are a complete invariant for a natural conjugacy class among the toy model family. We also establish a version of Singer’s theorem for the toy model family.

scholarly journals Projective subdynamics and universal shifts

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Pierre Guillon
Keyword(s):  
Large Class ◽  
Finite Type ◽  
Positive Entropy ◽  
Two Dimensional ◽  
One Dimensional ◽  
International Audience

International audience We study the projective subdynamics of two-dimensional shifts of finite type, which is the set of one-dimensional configurations that appear as columns in them. We prove that a large class of one-dimensional shifts can be obtained as such, namely the effective subshifts which contain positive-entropy sofic subshifts. The proof involves some simple notions of simulation that may be of interest for other constructions. As an example, it allows us to prove the undecidability of all non-trivial properties of projective subdynamics.

scholarly journals Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone

Logistics ◽  
2019 ◽  
Vol 3 (3) ◽  
pp. 17
Author(s):  
Todor Todorov
Keyword(s):  
Probability Density ◽  
Travel Time ◽  
Analytical Form ◽  
Two Dimensional ◽  
Travel Times ◽  
One Dimensional ◽  
Starting Point ◽  
Random Location ◽  
The Time Domain ◽  
Taxicab Geometry

Travel times for simple trips and cycles are analyzed for a storage/retrieval machine working in a one-dimensional or two-dimensional zone with taxicab geometry. A semi-random trip is defined as one-way travel from a known to a random location or vice versa. A random trip is defined as one-way travel from a random to another random location. The probability density function (PDF) of the travelling time for a semi-random trip in a one-dimensional zone is expressed analytically for all possible locations of its starting point. The PDF of a random trip within the same zone is found as a marginal probability by considering all possible durations for such travel. Then the PDFs for the travel times of single command (SC) and dual command (DC) cycles are obtained by scaling the PDF for the travel time of a semi-random trip (for SC) and as the maximum travel time of two independent semi-random trips (for DC). PDFs for travel times in a two-dimensional service zone with taxicab geometry are calculated by considering the trip as a superposition of two one-dimensional trips. The PDFs for travel times of SC and DC cycles are calculated in the same way. Both the one-dimensional and the two-dimensional service zones are analyzed in the time domain without normalization. The PDFs for all travel times are expressed in an analytical form parameterized by the maximal possible travel time within the zone. The graphs of all PDFs are illustrated by numerical examples.

scholarly journals Dynamical Behavior of Two Dimensional Hénon Maps

2012 ◽  
Vol 47 (1) ◽  
pp. 55-60
Author(s):  
MS Islam ◽  
MS Islam
Keyword(s):  
Fixed Points ◽  
Computer Programming ◽  
Dynamical Behavior ◽  
Periodic Points ◽  
Numerical Results ◽  
Two Dimensional ◽  
Henon Maps ◽  
Hénon Maps ◽  
Non Linear ◽  
Parameter Values

In this article, we study the two dimensional non-linear dynamical behavior of Hénon maps. We investigate the parameter values for which fixed points and periodic points of period two exist and study the dimension of the maps. We also investigate the numerical results of the maps and use computer programming Mathematica for generating graphs and computations. DOI: http://dx.doi.org/10.3329/bjsir.v47i1.10722 Bangladesh J. Sci. Ind. Res. 47(1), 55-60, 2012

ABRUPT DIMENSION CHANGES AT BASIN BOUNDARY METAMORPHOSES

1992 ◽  
Vol 02 (03) ◽  
pp. 533-541 ◽  
Author(s):  
BAE-SIG PARK ◽  
CELSO GREBOGI ◽  
YING-CHENG LAI
Keyword(s):  
Dynamical Systems ◽  
Numerical Experiments ◽  
System Parameter ◽  
Analytic Calculation ◽  
Two Dimensional ◽  
Qualitative Model ◽  
One Dimensional ◽  
Basin Boundary ◽  
Chaotic Dynamical Systems ◽  
Basin Boundaries

Basin boundaries in chaotic dynamical systems can be either smooth or fractal. As a system parameter changes, the structure of the basin boundary also changes. In particular, the dimension of the basin boundary changes continuously except when a basin boundary metamorphosis occurs, at which it can change abruptly. We present numerical experiments to demonstrate such sudden dimension changes. We have also used a one-dimensional analytic calculation and a two-dimensional qualitative model to explain such changes.

Rods, plates and shells

1968 ◽  
Vol 64 (3) ◽  
pp. 895-913 ◽  
Author(s):  
A. E. Green ◽  
N. Laws ◽  
P. M. Naghdi
Keyword(s):  
Continuum Mechanics ◽  
Three Dimensional ◽  
Elastic Rods ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Starting Point ◽  
Non Linear ◽  
Plates And Shells

AbstractWe discuss non-linear thermodynamical theories of rods and shells using the three-dimensional theory of classical continuum mechanics as a starting point. The three-dimensional theory is reduced to a two-dimensional theory for a shell, or plate, and a one-dimensional theory for a rod by employing an exact expansion for the displacement but an approximation for the temperature. For elastic rods and shells a method of approximation is suggested which brings the respective theories into correspondence with those of Green and Laws (1) and Green, Naghdi and Wain-wright(2).

scholarly journals On Gumbel limit for the length of reactive paths

2014 ◽  
Vol 15 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Yuri Bakhtin
Keyword(s):  
Limit Theorem ◽  
Scaling Limit ◽  
Two Dimensional ◽  
Exit Times ◽  
One Dimensional ◽  
Starting Point ◽  
Noise Limit

We give a new proof of the vanishing noise limit theorem for exit times of one-dimensional diffusions conditioned on exiting through a point separated from the starting point by a potential wall. We also prove a scaling limit for exit location in a model two-dimensional situation.

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.

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