Tropical and Idempotent Mathematics
About this Title
G. L. Litvinov and S. N. Sergeev, Editors
This volume is a collection of papers from the International Conference on Tropical and Idempotent Mathematics, held in Moscow, Russia in August 2007. This is a relatively new branch of mathematical sciences that has been rapidly developing and gaining popularity over the last decade.
Tropical mathematics can be viewed as a result of the Maslov dequantization applied to “traditional” mathematics over fields. Importantly, applications in econophysics and statistical mechanics lead to an explanation of the nature of financial crises. Another original application provides an analysis of instabilities in electrical power networks.
Idempotent analysis, tropical algebra, and tropical geometry are the building blocks of the subject. Contributions to idempotent analysis are focused on the Hamilton-Jacobi semigroup, the max-plus finite element method, and on the representations of eigenfunctions of idempotent linear operators. Tropical algebras, consisting of plurisubharmonic functions and their germs, are examined. The volume also contains important surveys and research papers on tropical linear algebra and tropical convex geometry.
Graduate students and research mathematicians interested in modern mathematics, including tropical methods and their applications.
Table of Contents
- Marianne Akian, Stéphane Gaubert and Alexander Guterman – Linear independence over tropical semirings and beyond [MR 2581511]
- Marianne Akian, Stéphane Gaubert and Vassili Kolokoltsov – The optimal assignment problem for a countable state space [MR 2581512]
- Daniele Alessandrini – Dequantization of real convex projective manifolds [MR 2581513]
- M. Ansola and M. J. de la Puente – Tropical conics for the layman [MR 2581514]
- Antonio Avantaggiati and Paola Loreti – Idempotent aspects of Hopf-Lax type formulas [MR 2581515]
- Peter Butkovič and Kin Po Tam – On some properties of the image set of a max-linear mapping [MR 2581516]
- Vladimir I. Danilov, Alexander V. Karzanov and Gleb A. Koshevoy – Tropical Plücker functions and their bases [MR 2581517]
- Nadir Farhi – A class of periodic minplus homogeneous dynamical systems [MR 2581518]
- Zur Izhakian – Basics of linear algebra over the extended tropical semiring [MR 2581519]
- Michael Joswig – Tropical convex hull computations [MR 2581520]
- B. Kh. Kirshtein – Complex roots of systems of tropical equations and stability of electrical power networks [MR 2581521]
- Victor Maslov – Dequantization, statistical mechanics and econophysics [MR 2581522]
- D. McCaffrey – Graph selectors and the max-plus finite element method [MR 2581523]
- William M. McEneaney – Complexity reduction, cornices and pruning [MR 2581524]
- Alexander Rashkovskii – Tropical analysis of plurisubharmonic singularities [MR 2581525]
- Sergeĭ Sergeev – Multiorder, Kleene stars and cyclic projectors in the geometry of max cones [MR 2581526]
- G. B. Shpiz and G. L. Litvinov – A tropical version of the Schauder fixed point theorem [MR 2581527]
- Edouard Wagneur, Laurent Truffet, Farba Faye and Mamadou Thiam – Tropical cones defined by max-linear inequalities [MR 2581528]
- Cormac Walsh – Minimum representing measures in idempotent analysis [MR 2581529]