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By varying a parameter of a one-dimensional piecewise smooth map, stableperiodic orbits are observed. In this paper, complete analytic characterizationof these stable periodic orbits is obtained. An interesting relationshipbetween the cardinality of orbits and their period is established. It is provedthat for any $n$, there exist $\phi(n)$ distinct admissible patterns ofcardinality $n$. An algorithm to obtain these distinct admissible patterns isoutlined. Additionally, a novel algorithm to find the range of parameter forwhich the orbit exists is proposed.

Analysis of Stable Periodic Orbits in 1-D Linear Piecewise Smooth Maps