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With the help of miniaturized GPS recorders I recorded 167 tracks of 48 individual pigeons during their flight from 6 different sites around Frankfurt. The experiments consisted of two main series of repeated releases from two sites 30 km north and south from the pigeons' home loft. From the site in the south the pigeons homed 12 times and from the site in the north 16 times. After the final release from these sites, the pigeons were released at 60 km distance from home. These additional sites were selected so that the pigeons would presumably fly over the previous release site with which they were highly familiar. After conclusion of the main series two additional releases were performed, one within the magnetic anomaly of the Vogelsberg and one in a magnetically quiet region. To make these releases comparable, both release sites were selected so that the distance from the home loft was 40 km. All data obtained during these experiments were subjected to a threefold analysis, mostly based on methods that I had developed by myself or adapted for this specific study. In the first step, data were analyzed traditionally, evaluating variables similar to those that can be found in current literature. I therefore calculated values that correspond to those obtained by visual observation, like virtual vanishing bearings and intervals after one minute and after 2.5 km. Additionally I calculated the efficiency of the flights and efficiencies for specific portions of each flight, to derive variables that describe the behavior after vanishing. In the second step, which served also as a preparation for the mathematical analysis, the flight of the pigeons was separated into distinctive phases of the flight by the so-called points of decision. The flight of the pigeon can usually be separated into an initial phase of flying about, a departure and/or final homing phase. In more complex cases, however, several points of decision and a multitude of intermediary phases can be defined. Yet, the initial phase, the departure phase and the final homing phase can be defined for all tracks and therefore have been selected as appropriate candidates for a thorough analysis. In the last step I employed the so-called method of time lag embedding to reconstruct the underlying navigational process of the pigeons' homing flight. This method is based on the principles of chaos theory and is regularly employed for the analysis of dynamic systems. Its application allows the reconstruction of the underlying processes from experimentally recorded data without any a priori knowledge of the underlying system itself. For these reconstructed systems I calculated characteristic properties which are unique for each system. These are the so-called correlation dimension, describing the complexity of the system, and the so-called largest Lyapunov exponent, describing its predictability. Based on the knowledge gathered from these reconstructions, I used a variation of the previous methods to identify navigational phases, by calculating the correlation dimension as a sliding mean over the complete track. From these data I then derived further characteristics of the underlying process, such as its precision and differences in complexity depending on the pigeon's current position. ...