On the set of periodic intervals of an interval map

2010 ◽  
Vol 15 (2-3) ◽  
pp. 378-381
Author(s):  
M. Matviichuk
Keyword(s):  
Interval Map

scholarly journals Constant slope maps on the extended real line

2017 ◽  
Vol 38 (8) ◽  
pp. 3145-3169 ◽  
Author(s):  
MICHAŁ MISIUREWICZ ◽  
SAMUEL ROTH
Keyword(s):  
Real Line ◽  
Half Line ◽  
Piecewise Monotone ◽  
Bounded Interval ◽  
Interval Map ◽  
Piecewise Continuous ◽  
Constant Slope

For a transitive countably piecewise monotone Markov interval map we consider the question of whether there exists a conjugate map of constant slope. The answer varies depending on whether the map is continuous or only piecewise continuous, whether it is mixing or not, what slope we consider and whether the conjugate map is defined on a bounded interval, half-line or the whole real line (with the infinities included).

scholarly journals The Power Ratio and the Interval Map: Spiking Models and Extracellular Recordings

1998 ◽  
Vol 18 (23) ◽  
pp. 10090-10104 ◽  
Author(s):  
Daniel S. Reich ◽  
Jonathan D. Victor ◽  
Bruce W. Knight
Keyword(s):  
Power Ratio ◽  
Extracellular Recordings ◽  
Interval Map

CHAOTIC BEHAVIOR OF INTERVAL MAPS AND TOTAL VARIATIONS OF ITERATES

2004 ◽  
Vol 14 (07) ◽  
pp. 2161-2186 ◽  
Author(s):  
GOONG CHEN ◽  
TINGWEN HUANG ◽  
YU HUANG
Keyword(s):  
Nonlinear Systems ◽  
Initial Data ◽  
Topological Entropy ◽  
Chaotic Behavior ◽  
Homoclinic Orbits ◽  
Oscillatory Behavior ◽  
Exponential Rate ◽  
Interval Maps ◽  
Interval Map ◽  
Sensitive Dependence

Interval maps reveal precious information about the chaotic behavior of general nonlinear systems. If an interval map f:I→I is chaotic, then its iterates fnwill display heightened oscillatory behavior or profiles as n→∞. This manifestation is quite intuitive and is, here in this paper, studied analytically in terms of the total variations of fnon subintervals. There are four distinctive cases of the growth of total variations of fnas n→∞:(i) the total variations of fnon I remain bounded;(ii) they grow unbounded, but not exponentially with respect to n;(iii) they grow with an exponential rate with respect to n;(iv) they grow unbounded on every subinterval of I.We study in detail these four cases in relations to the well-known notions such as sensitive dependence on initial data, topological entropy, homoclinic orbits, nonwandering sets, etc. This paper is divided into three parts. There are eight main theorems, which show that when the oscillatory profiles of the graphs of fnare more extreme, the more complex is the behavior of the system.

AN ALGORITHM TO COMPUTE THE TOPOLOGICAL ENTROPY OF A UNIMODAL MAP

1999 ◽  
Vol 09 (09) ◽  
pp. 1881-1882 ◽  
Author(s):  
HENK BRUIN
Keyword(s):  
Topological Entropy ◽  
Unimodal Map ◽  
Interval Map

We describe an algorithm, due to F. Hofbauer, to compute the topological entropy of a unimodal interval map.

The cardiac memory “using the body surface activation recovery interval map”

2003 ◽  
Vol 9 (5) ◽  
pp. S54
Author(s):  
Wakaya Fujiwara ◽  
Kenji Tamura ◽  
Satoshi Kakizawa ◽  
Osamu Inami ◽  
Takahisa Kondo ◽  
...  
Keyword(s):  
Body Surface ◽  
The Body ◽  
Surface Activation ◽  
Cardiac Memory ◽  
Recovery Interval ◽  
Interval Map

The Strongly Simple Cycles with Given Rotation Pairs of an Interval Map

2006 ◽  
Vol 23 (1) ◽  
pp. 37-40
Author(s):  
Tai Xiang Sun ◽  
Hong Jian Xi ◽  
Xiao Yan Zhang
Keyword(s):  
Interval Map

TOPOLOGICAL ENTROPY FOR MULTIDIMENSIONAL PERTURBATIONS OF ONE-DIMENSIONAL MAPS

2001 ◽  
Vol 11 (05) ◽  
pp. 1443-1446 ◽  
Author(s):  
MICHAŁ MISIUREWICZ ◽  
PIOTR ZGLICZYŃSKI
Keyword(s):  
Topological Entropy ◽  
Positive Entropy ◽  
One Dimensional ◽  
Interval Map ◽  
One Dimensional Maps

We prove that if an interval map of positive entropy is perturbed to a compact multidimensional map then the topological entropy cannot drop down considerably if the perturbation is small.

An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps

1994 ◽  
Vol 14 (4) ◽  
pp. 621-632 ◽  
Author(s):  
V. Baladi ◽  
D. Ruelle
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Constant Weight ◽  
Piecewise Constant ◽  
Piecewise Monotone ◽  
Interval Maps ◽  
Interval Map ◽  
Piecewise Continuous

AbstractWe consider a piecewise continuous, piecewise monotone interval map and a piecewise constant weight. With these data we associate a weighted kneading matrix which generalizes the Milnor—Thurston matrix. We show that the determinant of this matrix is related to a natural weighted zeta function.

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