Abstract. The results of this paper relate the dynamics of a continuous map/of the interval and the topology of the inverse limit space with bonding map /. These inverse limit spaces have been studied by many authors, and are examples of what Bing has called "snakelike continua". Roughly speaking, we show that when the dynamics of / are complicated, the inverse limit space contains indecomposable subcontinua. We also establish a partial converse.
Abstract.The purpose of this note is to show that every inverse limit space of an interval mapping can be realized as a global attractor for a homeomorphism of the plane.
The eigenvalues of the Kirchhoff matrix for a molecule consisting of m chains and μ multifunctional junctions can be calculated from a reduced matrix of dimension μ×μ. Many of the eigenvalues for complicated molecules can be obtained exactly, and the remainder are accessible by numerical methods. We find small eigenvalues for trifunctional networks which can be associated with very slowly relaxing oscillations in gels. In addition, networks have μ high frequency modes, which are located in unique regions of the spectrum.
Abstract. The results of this paper relate the dynamics of a continuous map/of the interval and the topology of the inverse limit space with bonding map /. These inverse limit spaces have been studied by many authors, and are examples of what Bing has called "snakelike continua". Roughly speaking, we show that when the dynamics of / are complicated, the inverse limit space contains indecomposable subcontinua. We also establish a partial converse.
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