Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Integrable Systems: A Celebration of Emma Previato’s 65th Birthday
- 1 Trace Ideal Properties of a Class of Integral Operators
- 2 Explicit Symmetries of the Kepler Hamiltonian
- 3 A Note on the Commutator of Hamiltonian Vector Fields
- 4 Nodal Curves and a Class of Solutions of the Lax Equation for Shock Clustering and Burgers Turbulence
- 5 Solvable Dynamical Systems in the Plane with Polynomial Interactions
- 6 The Projection Method in Classical Mechanics
- 7 Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets
- 8 Bi-Flat F-Manifolds: A Survey
- 9 The Periodic 6-Particle Kac-van Moerbeke System
- 10 Integrable Mappings from a Unified Perspective
- 11 On an Arnold-Liouville Type Theorem for the Focusing NLS and the Focusing mKdV Equations
- 12 Commuting Hamiltonian Flows of Curves in Real Space Forms
- 13 The Kowalewski Top Revisited
- 14 The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem
- 15 Tropical Markov Dynamics and Cayley Cubic
- 16 Positive One–Point Commuting Difference Operators∗†
15 - Tropical Markov Dynamics and Cayley Cubic
Published online by Cambridge University Press: 19 March 2020
Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Integrable Systems: A Celebration of Emma Previato’s 65th Birthday
- 1 Trace Ideal Properties of a Class of Integral Operators
- 2 Explicit Symmetries of the Kepler Hamiltonian
- 3 A Note on the Commutator of Hamiltonian Vector Fields
- 4 Nodal Curves and a Class of Solutions of the Lax Equation for Shock Clustering and Burgers Turbulence
- 5 Solvable Dynamical Systems in the Plane with Polynomial Interactions
- 6 The Projection Method in Classical Mechanics
- 7 Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets
- 8 Bi-Flat F-Manifolds: A Survey
- 9 The Periodic 6-Particle Kac-van Moerbeke System
- 10 Integrable Mappings from a Unified Perspective
- 11 On an Arnold-Liouville Type Theorem for the Focusing NLS and the Focusing mKdV Equations
- 12 Commuting Hamiltonian Flows of Curves in Real Space Forms
- 13 The Kowalewski Top Revisited
- 14 The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem
- 15 Tropical Markov Dynamics and Cayley Cubic
- 16 Positive One–Point Commuting Difference Operators∗†
Summary
We study the tropical version of Markov dynamics on the Cayley cubic, introduced by V. E. Adler and one of the authors. We show that this action is semi-conjugated to the standard action of $SL_2(\mathbb Z)$ on a torus, and thus is ergodic with the Lyapunov exponent and entropy given by the logarithm of the spectral radius of the corresponding matrix.
- Type
- Chapter
- Information
- Integrable Systems and Algebraic Geometry , pp. 383 - 394Publisher: Cambridge University PressPrint publication year: 2020