Title of dissertation: QUASIPERIODICITY AND CHAOS Suddhasattwa Das, Doctor of Philosophy, 2015 Dissertation directed by: Professor James A. Yorke Department of Mathematics In this work, we investigate a property called “multi-chaos” is which a chaotic set has densely many hyperbolic periodic points of unstable dimension k embedded in it, for at least 2 different values of k. We construct a fami...

We show that graph map with zero topological entropy is Li-Yorke chaotic if and only it has an NS-pair (a pair of non-separable points containing in a same solenoidal $\omega$-limit set), non-diagonal IN-pair IT-pair. This completes characterization sequence for maps.

A relatively small number of mathematically simple maps and flows are routinely used as examples of low-dimensional chaos. These systems typically have a number of parameters that are chosen for historical or other reasons. This paper addresses the question of whether a different choice of these parameters can produce strange attractors that are significantly more chaotic (larger Lyapunov expon...

A variant of the Hénon map is described in which the linear term is replaced by one that involves a much earlier iterate of the map. By varying the time delay, this map can be used to explore the transition from low-dimensional to high-dimensional dynamics in a chaotic system with minimal algebraic complexity, including a detailed comparison of the Kaplan-Yorke and correlation dimensions. The h...

In this paper we examine a very simple and elegant example of high-dimensional chaos in a coupled array of flows in ring architecture that is cyclically symmetric and can also be viewed as an N-dimensional spatially infinite labyrinth (a "hyperlabyrinth"). The scaling laws of the largest Lyapunov exponent, the Kaplan-Yorke dimension, and the metric entropy are investigated in the high-dimension...

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits (T ) of a dynamical system scales as a function of computer precision (ε) and the correlation dimension (d) of the chaotic attractor: T ∼ ε. In this work, we are concerned with increasing the average p...

Combinatorial techniques are applied to the symbolic dynamics representing transient chaotic behavior in tent maps in order to solve the problem of Ott-Grebogi-Yorke control to the nontrivial fixed point occurring in such maps. This approach allows "preimage overlap" to be treated exactly. Closed forms for both the probability of control being achieved and the average number of iterations to co...

In this paper we apply the techniques of symbolic dynamics to the analysis of a labor market which shows large volatility in employment flows. In a recent paper, Bhattacharya and Bunzel [1] have found that the discrete time version of the Pissarides-Mortensen matching model can easily lead to chaotic dynamics under standard sets of parameter values. To conclude about the existence of chaotic dy...