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Showing 1 to 16 of 16 for “"Topological Entropy"”.
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Topological entropy of the Lozi family
Thesis (Ph. D.)--Michigan State University. Mathematics, 2010
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Topological entropy bounds for switched linear systems with lie structure
… provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time horizons, in the limit. After working out entropy computations in detail for …
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On the topological entropy of nilpotent groups of finite rank
… deals with some finiteness conditions on the topological entropy of continuous endomorphims of periodic locally compact Heisenberg p-groups (p prime). These are relevant models of locally compact nilpotent groups and their structure may be described very well by semidirect products. Firstly, …
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Switched and hybrid systems with inputs: small-gain theorems, control with limited information, and topological entropy
… stabilize a linear time-invariant system and its topological entropy, we examine a notion of topological entropy for switched systems with a known switching signal. This notion is formulated in terms of the number of initial points such that the corresponding trajectories approximate all …
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Topics of entropy in locally compact abelian groups
… group theory in connection with recent topics of topological entropy of locally compact abelian groups. It has been used the reference of [D. J. S. Robinson, A Course in the Theory of Groups, Springer, 1996, New York], which is a classical textbook in group theory. A list of exercises, relevant to …
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Core Entropy of Finite Subdivision Rules
The topological entropy of the subdivision map of a finite subdivision rule restricted to the 1-skeleton of its model subdivision complex, which we call textbf{core entropy}, is examined. We consider core entropy for finite subdivision rules realizing quadratic Misiurewicz polynomials and matings …
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Study of the dynamics of transport and mixing using set oriented methods
… groups. One can predict a lower bound on the topological entropy (i.e. exponential rate of stretching of material lines) of flows (h<sub>f</sub>) by applying the Thurston-Nielsen classification theorems to these braids. This gives a reduced order model for the dynamics of transport of the …
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Studies of one-dimensional unimodal maps in the chaotic regime
… alphabet and the approach of cycle expansion the topological entropy can be easily computed. Furthermore, the scaling properties of the measure of constant topological entropy are studied. Our results support the conjectures that for the maps with the same order of maximum, the asymptotic behavior …
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Pullback of currents by meromorphic maps
… which is invariant under $f$ and has maximal entropy (i.e. the entropy of the measure equals the topological entropy). The same question is harder to answer for a general meromorphic map $f$, due to the fact that $f$ is not continuous. Since the pioneer work of Bedford et al. on H\'enon maps, …
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Surface Entropy of Shifts of Finite Type
… : χ x R → [0,∞] which we call the surface entropy of a shift. This definition is inspired by the topological entropy of a subshift and we compare and contrast several structural properties of surface entropy to entropy. We demonstrate that much like entropy, the finiteness of surface …
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State estimation of switched nonlinear systems and systems with bounded inputs: Entropy and bit rates
… In this thesis, we present two notions of entropy for state estimation of nonlinear switched and non-autonomous dynamical systems as lower bounds on the average number of bits needed to be sent from the sensors to the estimators to estimate the states with deterministic (worst case) error …
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Braiding of Coronal Loops and Consequences for Coronal Heating
… coronal fields. We used the concepts of topological entropy and helicity to categorise the drivers and applied them to a uniform field representing a simple coronal loop. We found that both complexity of driving and ability to inject helicity are key to the type of evolution which takes …
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Ergodic properties of countable extensions
… given interval map to be continuous, Markov, and topologically mixing, and show by example that the mixing hypothesis is essential. ^ Next, we study a class of countable state subshifts of finite type which admit finite-state factors. Our systems carry a displacement function, analogous to that …
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Computational Intelligence and Complexity Measures for Chaotic Information Processing
… Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov …
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Topological Chaos and Mixing in Lid-Driven Cavities and Rectangular Channels
… in these systems to enhance mixing efficiency. Topological chaos can also lead to efficient and rapid mixing. In this dissertation, an approach to enhance fluid mixing in laminar flows without internal rods is demonstrated by using the idea of topological chaos. Periodic motion of three stirrers …