ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes

81. Thomas Wanner:
    ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes
    Julia Package Manual, GitHub, 202 pages, 2025.

Abstract

This is an extensive manual for the Julia package ConleyDynamics.jl, which can be used to study combinatorial multivector fields using Conley theory. The multivector fields can be defined on arbitrary Lefschetz complexes, including both simplicial and cubical complexes as important special cases. It provides tools for the computation of Conley indices, connection matrices, and Conley-Morse graphs. In addition, homology over finite fields and the rationals can be computed, including persistent homology and relative homology. The algorithms rely on a built-in sparse matrix implementation which is geared towards computations over finite fields and the rationals. The manual presents not only a description of the package, but also of the required background material.

Links

The manual can be accessed here. It can also be downloaded as a book in pdf format.

Bibtex

@book{conleydynamics:manual,
  author = {Thomas Wanner},
  title = {{C}onley{D}ynamics.jl: {A} {J}ulia package for multivector
           dynamics on {L}efschetz complexes},
  publisher = {Julia Package Manual},
  url = {https://github.com/almost6heads/ConleyDynamics.jl},
  year = {2025}
  }