Live briefing
Everything about Integrable system
Property of certain dynamical systems
In mathematics, integrability is a property of certain dynamical systems, that means very roughly that the solutions of the system are "simple" enough that they can be written down exactly. More precisely, while there are several distinct formal definitions, an integrable system can be thought of as a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space. Integrable systems are in this sense the opposite of chaotic systems, where small changes in initial conditions create wild deviations in the phase space behavior of solutions. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Integrable systemA 5-minute orientation
- Skim a recent paper: A biological definition of neuronal α-synuclein disease: towards an integrated staging system for researchInfluential work since 2022
- Pick up a classic book: Control and Dynamic SystemsThe most-reprinted book on the subject
- Read the landmark paper: Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanesCited 20,362 times
- Go sideways: Action-angle coordinatesA closely related topic
- Go sideways: Poisson bracketA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
- General dynamical systems
- Hamiltonian systems and Liouville integrability
- Action-angle variables
- The Hamilton–Jacobi approach
- Solitons and inverse spectral methods
- Hirota bilinear equations and τ-functions
- Algebraic integrability
- Diophantine integrability
- Quantum integrable systems
- Exactly solvable models
- List of some well-known integrable systems
🏆 Landmark papers (most cited)
Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes
Generalized Thermalization in an Integrable Lattice System
A Generalization of Coupled Integrable, Dispersionless System
Is free-surface hydrodynamics an integrable system?
The Pentagram Map: A Discrete Integrable System
KdV6: An integrable system
An interpolating dispersionless integrable system
An integrable Hamiltonian system
🆕 Influential since 2022
A biological definition of neuronal α-synuclein disease: towards an integrated staging system for research
The SHARK integral generation and digestion system
Microglia regulate central nervous system myelin growth and integrity
Low carbon optimal operation of integrated energy system based on carbon capture technology, LCA carbon emissions and ladder-type carbon trading
📚 Books worth reading
Control and Dynamic SystemsCornelius T. Leondes · 1985
ESDSteven H. Voldman · 2005
System dynamicsDean Karnopp, Dean C. Karnopp · 1975
Physics and Technology of Crystalline Oxide Semiconductor CAAC-IGZONoboru Kimizuka, Shunpei Yamazaki · 2016
System IntegrationKurt Hoffmann, Kurt Hoffmann · 2003- 📕Analysis and Design of Analog Integrated CircuitsPaul R. Gray · 1992
- 📕Engineering systems integrationGary O. Langford · 2012
Automation, Production Systems, and Computer-Integrated ManufacturingMikell P. Groover · 1987
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Action-angle coordinates In classical mechanics, action-angle variables are a set of canonical coordinates that are useful in characterizing the nature of commuting flows in integrable…
- Poisson bracket In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's…
- Canonical quantum gravity In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity). It is a Hamiltonian…
- Hamiltonian mechanics In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian…
- Dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric…
- Method of quantum characteristics Quantum characteristics are phase-space trajectories that arise in the phase space formulation of quantum mechanics through the Wigner transform of Heisenberg…
- Liouville–Arnold theorem The Liouville–Arnold theorem is a result in classical mechanics which says, roughly speaking, that seemingly complicated systems can be described as combination…
- Lax pair In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential…