HORODIMORPHISM Meaning and
Definition
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Horodimorphism is a mathematical term that refers to a concept in the theory of dynamical systems. It describes a certain type of isomorphism or equivalence between two different dynamical systems. In particular, horodimorphism focuses on the behavior of points at infinity in these systems.
In the context of horodimorphism, the term "horosphere" is essential. A horosphere is a geometric construct that represents a surface in a hyperbolic space, centered at a point at infinity. Horodimorphism studies the relationship between these horospheres in different dynamical systems.
When two dynamical systems are said to be horodimorphic, it means that there is an isomorphism or equivalence that preserves the horospheres of each system. In other words, the horospheres in one system can be mapped onto the horospheres of the other system in a way that respects their respective properties.
This concept of horodimorphism is widely used in the study of hyperbolic dynamics and geometric group theory. It helps to understand and classify the behavior and properties of dynamical systems in relation to their horospheres. By examining the horospheric relationship between systems, mathematicians are able to make significant advancements in the understanding of these complex mathematical structures.
