Jean-Pierre Aubin (1991), Viability Theory, Boston: Birkhäuser; reprinted 2009 in Modern Birkhäuser Classics — DOI-10.1007/978-0-8176-4910-4
Key takeaways
Registered from metadata, not a reading. What the record knows of the book’s content comes from the author’s mini-course notes (LIT-714), which cite it as their general reference (“chapter 8 of [2, Aubin]”) and state the same core definitions in the simpler setting of differential equations:
- An evolution is viable in a set K if it stays in K. K is viable under a system if from every state of K at least one evolution stays in K, and invariant if every evolution does.
- The viability kernel of K is the set of states of K from which at least one evolution stays in K for ever. It is the largest viable subset of K.
- The capture basin of a target C is the set of states from which some evolution reaches C in finite time; the viable-capture basin requires it to stay in K until it does.
The book itself works with differential inclusions, where a state admits many evolutions, which is where the difference between viability (one evolution suffices) and invariance (all evolutions must) does real work.
Standing in the record
Filed on 2026-10-05 at the owner’s request, as one of the works an essay on will and organization cites that the record did not hold (the essay’s §6.1, “stability is not viability”). The record’s account of the distinction is THEORY-134, sourced on the notes, not on this book.
Deferred because it was not read. The 2011 New Directions volume
(Aubin, Bayen & Saint-Pierre) is the more current statement and would be
the better book to read if a copy is supplied.