Halving dynamical systems
Shaun Stevens, Tom Ward, Stefanie Zegowitz
TL;DR
This paper investigates how the dynamics and growth of closed orbits are affected when one system is derived from another via an involution quotient, revealing constraints and freedoms in their relationship.
Contribution
It introduces a framework for understanding the relationship between dynamical systems connected through involution quotients, focusing on orbit growth and structural constraints.
Findings
Identifies constraints on orbit growth in quotient systems
Explores the extent of freedom in dynamical relationships
Provides theoretical insights into involution-based system relationships
Abstract
The relationship between two dynamical systems, one of which is obtained from the other by forming the quotient by an action of an involution commuting with the dynamics, is studied. The constraints and the possible extent of freedom in the relationship between the growth of closed orbits in pairs of systems related in this way is explored.
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