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REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
2015/9/29
An important discovery of the 20th century mathematics is that many deterministic
systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
NEW EXAMPLES OF S-UNIMODAL MAPS WITH A SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
S-UNIMODAL MAPS SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
2015/9/25
We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps ϕ which do not have a finite absolutely continuous invariant measure, but do have...
NEW EXAMPLES OF TOPOLOGICALLY EQUIVALENT S-UNIMODAL MAPS WITH DIFFERENT METRIC PROPERTIES
TOPOLOGICALLY EQUIVALENT S-UNIMODAL MAPS DIFFERENT METRIC PROPERTIES
2015/9/25
We construct examples of topologically conjugate unimodal maps, such that both of them have an absolutely continuous invariant measure, but for one of them that measure is finite, and for another one ...
Computing the topological entropy of unimodal maps
Topological entropy interval maps symbolic dynamics
2011/3/2
We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm
is obtained by t...
Computing the topological entropy of unimodal maps
Topological entropy interval maps symbolic dynamics
2010/12/28
We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm
is obtained by t...
Dynamics of continued fractions and kneading sequences of unimodal maps
Dynamics of continued fractions kneading sequences of unimodal maps
2011/1/20
The goal of this paper is to provide a link between the parameter spaces of two families of one-dimensional dynamical systems, and to shed some light onto some sets of numbers which arise as “exceptio...
Reduction of Dietrich-Ruina attractors to unimodal maps
Reduction of Dietrich-Ruina attractors unimodal maps
2009/11/13
We present a geometric analysis of a quasi-static single degree of freedom elastic slider with a state and rate dependent friction law. In particular, we examine and characterize the regime of chaotic...