The increasing number of objects orbiting the earth justifies the great attention and interest in the observation, spacecraft protection, and collision avoidance. These studies involve different disturbances and resonances in the orbital motions of these objects distributed by the distinct altitudes. In this work, objects in resonant orbital motions are studied in low earth orbits. Using the twoline elements (TLE) of the NORAD, resonant angles and resonant periods associated with real motions are described, providing more accurate information to develop an analytical model that describes a certain resonance. The time behaviors of the semimajor axis, eccentricity, and inclination of some space debris are studied. Possible irregular motions are observed by the frequency analysis and by the presence of different resonant angles describing the orbital dynamics of these objects.

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We introduce the notion of conductance in discrete dynamical systems defined by iterated maps of the interval. Our starting point is the notion of conductance in the graph theory. We pretend to apply the known results in this new context.

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A network of chaotic dynamical systems may synchronize. For some networks there is the possibility that, coupling a new node to the network, the synchronization will be commanded by that new node. That possibility depends on the network and on the way the new node is coupled to the network. We consider a coupling that can provide what we call a full-commanding and we define the corresponding full-commandwindow. The limit situations corresponding to a completely connected network and to a completely disconnected one provide us some understanding about what makes a network more receptive or more resistant to commanding.