Explore the theoretical framework of seismic base isolation techniques used in the design of earthquake$-$resistant structures. Describe the different types of base isolators, such as elastomeric bearings and sliding bearings, and explain the mechanical behavior and performance characteristics of each type. Discuss the mathematical modeling of base$-$isolated systems, including the concepts of modal analysis and time$-$history analysis. Furthermore, evaluate the advantages and limitations of base isolation compared to traditional fixed$-$base designs, considering factors such as cost$,$ maintenance, and applicability to various types of buildings.