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The aim of this chapter is to provide new insights of the return map of a given ellipse E. The main tool of this approach is the eccentricity \(\varepsilon \) of E and hence various expressions and transformations of \(\varepsilon \) are used in order to obtain new aspects concerning both the return map and the associated delta map. Also, we study the return map in the setting of plane hyperbolic geometry.

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The Return Map of an Ellipse: New Theoretical and Practical Aspects

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  • 发表日期：

    2025年

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  • Mircea Crasmareanu

摘要

The aim of this chapter is to provide new insights of the return map of a given ellipse E. The main tool of this approach is the eccentricity \(\varepsilon \) of E and hence various expressions and transformations of \(\varepsilon \) are used in order to obtain new aspects concerning both the return map and the associated delta map. Also, we study the return map in the setting of plane hyperbolic geometry.