Charles Conley, known for his work in dynamical systems theory, developed the Conley index theory to analyze the topological structure of invariant sets of diffeomorphisms and smooth flows. This theory, a broad extension of the Hopf index theorem, has significant applications in the study of dynamics, including the existence of periodic orbits in Hamiltonian systems, traveling wave solutions for partial differential equations, and the proof of chaotic behavior in dynamical systems. One key aspect of Conley's theory is the concept of isolating neighborhoods and isolated invariant sets, which form the basis for the computation of the Conley index. This index, independent of the choice of index pair, is invariant under certain deformations of the dynamical system, making it a powerful tool in the study of dynamical systems. Conley's work laid the foundation for the development of Floer homology and has had a profound impact on the understanding of complex dynamical systems.

Conley is a versatile name with various associations, including an Irish surname and a range of buildings, bridges, and roads across the United States. Notable examples include the John D. Conley House in Laramie, WY, and the Sanford F. Conley House in Columbia, MO, both listed on the National Register of Historic Places (NRHP). Furthermore, the Conley-Greene Rockshelter in Lytten, KY, and Conley's Ford Covered Bridge in Parke County, IN, showcase the diverse historical and architectural significance of the Conley name. In addition to physical structures, Conley has legal relevance, such as in the case Conley v. Gibson, decided by the Supreme Court of the United States in 1957. Moreover, Conley has geographical ties to places like Conley, Georgia, and Conley Township, Holt County, Nebraska. Educational institutions like Conley-Caraballo High School and J. Michael Conley Elementary School at Southwood also bear the Conley name. Finally, the name extends to the natural world with Conleyus, a genus of crabs named after the collector Harry T. Conley.

Conley Francis Byrd Sr. (January 14, 1925 – July 19, 2014) was an esteemed figure who served as a justice of the Arkansas Supreme Court from 1967 to 1980. Hailing from Poughkeepsie, Arkansas, Byrd's early years were marked by hard work as he began picking cotton on his family's farm at the tender age of six. Following his high school graduation in 1943, he bravely joined the U.S. Navy and served in the South Pacific Theatre during World War II, notably on the destroyer escort USS Harold C. Thomas (DE-21). Byrd's pursuit of education led him to Arkansas State College, Arkansas State Teachers College, and culminated in obtaining his law degree from the University of Arkansas School of Law in 1950. His illustrious career on the Arkansas Supreme Court spanned thirteen years before his retirement in 1979 due to health concerns. Throughout his tenure, Byrd made significant contributions to the legal landscape, leaving a lasting impact on the judicial system.

Conley Erwin Greear (March 2, 1887 – April 12, 1966) was an American politician and dentist from Virginia who made significant contributions in his lifetime. Born in Wood, Scott County, Virginia, Greear pursued his education at Emory and Henry College and the Medical College of Virginia, earning a D.D.S. He dedicated 56 years to dentistry, practicing in Fort Blackmore, and also served as a member of the Virginia House of Delegates, representing Scott County from 1954 to 1958. Despite his political and professional endeavors, Greear cherished his family life, being survived by his son, Marion Carter, and daughter, Louise. His commitment to public service and his community was evident in his active involvement as a Republican and a member of the Baptist faith. Greear's legacy lives on, and his impact is remembered after his passing on April 12, 1966. He was laid to rest in Holston View Cemetery.