| 37-XX | | Prev: 35 | Up: Top | Next: 39 | |
| Dynamical systems and ergodic theory [xref: 34Cxx, 34Kxx, 39B12, 57Sxx, 58Kxx, 70Gxx, 70Kxx, 76F20, 76Fxx] | |
| [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] |
37-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 37-01
| Instructional exposition (textbooks, tutorial papers, etc.)
| 37-02
| Research exposition (monographs, survey articles)
| 37-03
| Historical (must also be assigned at least one classification number from Section 01)
| 37-04
| Explicit machine computation and programs (not the theory of computation or programming)
| 37-06
| Proceedings, conferences, collections, etc.
| |
37Axx
| Ergodic theory [See also 28Dxx]
[xref: 22F10, 28Dxx, 37H05, 37H15, 47A35]
| 37A05 |
Measure-preserving transformations
| 37A10 |
One-parameter continuous families of measure-preserving transformations
| 37A15 |
General groups of measure-preserving transformation [See mainly 22Fxx]
| 37A17 |
Homogeneous flows [See also 22Fxx]
| 37A20 |
Orbit equivalence, cocycles, ergodic equivalence relations
| 37A25 |
Ergodicity, mixing, rates of mixing
| 37A30 |
Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}
| 37A35 |
Entropy and other invariants, isomorphism, classification
| 37A40 |
Nonsingular (and infinite-measure preserving) transformations
| 37A45 |
Relations with number theory and harmonic analysis [See also 11Kxx]
| 37A50 |
Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]
| 37A55 |
Relations with the theory of $C^*$-algebras [See mainly 46L55]
| 37A60 |
Dynamical systems in statistical mechanics [See also 82Cxx]
| 37A99 |
None of the above, but in this section
| |
37Bxx
| Topological dynamics [See also 54H20]
[xref: 26A18, 54H20]
| 37B05 |
Transformations and group actions with special properties (minimality, distality, proximality, etc.)
| 37B10 |
Symbolic dynamics [See also 37Cxx, 37Dxx]
| 37B15 |
Cellular automata
[xref: 68Q80]
| 37B20 |
Notions of recurrence
| 37B25 |
Lyapunov functions and stability; atrractors, repellers
| 37B30 |
Index theory, Morse-Conley indices
| 37B35 |
Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
| 37B40 |
Topological entropy
| 37B45 |
Continua theory in dynamics
| 37B50 |
Multi-dimensional shifts of finite type, tiling dynamics
| 37B55 |
Nonautonomous dynamical systems
[xref: 37C60]
| 37B99 |
None of the above, but in this section
| |
37Cxx
| Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
[xref: 26A18, 35B30, 37B10, 37H15]
| 37C05 |
Smooth mappings and diffeomorphisms
| 37C10 |
Vector fields, flows, ordinary differential equations
[xref: 57R27]
| 37C15 |
Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
| 37C20 |
Generic properties, structural stability
[xref: 34D30]
| 37C25 |
Fixed points, periodic points, fixed-point index theory
| 37C27 |
Periodic orbits of vector fields and flows
| 37C29 |
Homoclinic and heteroclinic orbits
| 37C30 |
Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
| 37C35 |
Orbit growth
| 37C40 |
Smooth ergodic theory, invariant measures [See also 37Dxx]
| 37C45 |
Dimension theory of dynamical systems
| 37C50 |
Approximate trajectories (pseudotrajectories, shadowing, etc.)
| 37C55 |
Periodic and quasiperiodic flows and diffeomorphisms
| 37C60 |
Nonautonomous smooth dynamical systems [See also 37B55]
| 37C65 |
Monotone flows
| 37C70 |
Attractors and repellers, topological structure
[xref: 34D45]
| 37C75 |
Stability theory
[xref: 34Dxx]
| 37C80 |
Symmetries, equivariant dynamical systems
| 37C85 |
Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
| 37C99 |
None of the above, but in this section
| |
37Dxx
| Dynamical systems with hyperbolic behavior
[xref: 34C28, 37B10, 37C40, 37H15, 81Q50]
| 37D05 |
Hyperbolic orbits and sets
| 37D10 |
Invariant manifold theory
| 37D15 |
Morse-Smale systems
| 37D20 |
Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
| 37D25 |
Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
| 37D30 |
Partially hyperbolic systems and dominated splittings
| 37D35 |
Thermodynamic formalism, variational principles, equilibrium states
| 37D40 |
Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
| 37D45 |
Strange attractors, chaotic dynamics
[xref: 34D45, 70K55]
| 37D50 |
Hyperbolic systems with singularities (billiards, etc.)
| 37D99 |
None of the above, but in this section
| |
37Exx
| Low-dimensional dynamical systems
[xref: 26A18]
| 37E05 |
Maps of the interval (piecewise continuous, continuous, smooth)
| 37E10 |
Maps of the circle
| 37E15 |
Combinatorial dynamics (types of periodic orbits)
| 37E20 |
Universality, renormalization [See also 37F25]
| 37E25 |
Maps of trees and graphs
| 37E30 |
Homeomorphisms and diffeomorphisms of planes and surfaces
| 37E35 |
Flows on surfaces
| 37E40 |
Twist maps
| 37E45 |
Rotation numbers and vectors
| 37E99 |
None of the above, but in this section
| |
37Fxx
| Complex dynamical systems [See also 30D05, 32Hxx]
[xref: 28A80, 30D05]
| 37F05 |
Relations and correspondences
| 37F10 |
Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
| 37F15 |
Expanding maps; hyperbolicity; structural stability
| 37F20 |
Combinatorics and topology
| 37F25 |
Renormalization
[xref: 37E20]
| 37F30 |
Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
| 37F35 |
Conformal densities and Hausdorff dimension
| 37F40 |
Geometric limits
| 37F45 |
Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
| 37F50 |
Small divisors, rotation domains and linearization; Fatou and Julia sets
| 37F75 |
Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]
| 37F99 |
None of the above, but in this section
| |
37Gxx
| Local and nonlocal bifurcation theory [See also 34Cxx]
[xref: 34C23, 35B32, 37H20]
| 37G05 |
Normal forms
| 37G10 |
Bifurcations of singular points
| 37G15 |
Bifurcations of limit cycles and periodic orbits
| 37G20 |
Hyperbolic singular points with homoclinic trajectories
| 37G25 |
Bifurcations connected with nontransversal intersection
| 37G30 |
Infinite nonwandering sets arising in bifurcations
| 37G35 |
Attractors and their bifurcations
| 37G40 |
Symmetries, equivariant bifurcation theory
| 37G99 |
None of the above, but in this section
| |
37Hxx
| Random dynamical systems [See also 15A52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]
| 37H05 |
Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]
| 37H10 |
Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]
| 37H15 |
Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]
| 37H20 |
Bifurcation theory [See also 37Gxx]
| 37H99 |
None of the above, but in this section
| |
37Jxx
| Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]
[xref: 53Dxx, 70Hxx]
| 37J05 |
General theory, relations with symplectic geometry and topology
| 37J10 |
Symplectic mappings, fixed points
| 37J15 |
Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]
| 37J20 |
Bifurcation problems
| 37J25 |
Stability problems
| 37J30 |
Obstructions to integrability (nonintegrability criteria)
| 37J35 |
Completely integrable systems, topological structure of phase space, integration methods
[xref: 35Q58, 81R12]
| 37J40 |
Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion
| 37J45 |
Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
| 37J50 |
Action-minimizing orbits and measures
| 37J55 |
Contact systems [See also 53D10]
| 37J60 |
Nonholonomic dynamical systems [See also 70F25]
| 37J99 |
None of the above, but in this section
| |
37Kxx
| Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]
[xref: 34Gxx, 46L55, 47J35, 70Sxx]
| 37K05 |
Hamiltonian structures, symmetries, variational principles, conservation laws
| 37K10 |
Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
[xref: 35Q53, 35Q55, 35Q58]
| 37K15 |
Integration of completely integrable systems by inverse spectral and scattering methods
| 37K20 |
Relations with algebraic geometry, complex analysis, special functions [See also 14H70]
| 37K25 |
Relations with differential geometry
| 37K30 |
Relations with infinite-dimensional Lie algebras and other algebraic structures
| 37K35 |
Lie-Bäcklund and other transformations
| 37K40 |
Soliton theory, asymptotic behavior of solutions
[xref: 35Q51]
| 37K45 |
Stability problems
| 37K50 |
Bifurcation problems
[xref: 35B32]
| 37K55 |
Perturbations, KAM for infinite-dimensional systems
| 37K60 |
Lattice dynamics [See also 37L60]
[xref: 37L60, 82C23]
| 37K65 |
Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
| 37K99 |
None of the above, but in this section
| |
37Lxx
| Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]
[xref: 46L55, 47J35, 58D25, 70Sxx]
| 37L05 |
General theory, nonlinear semigroups, evolution equations
| 37L10 |
Normal forms, center manifold theory, bifurcation theory
| 37L15 |
Stability problems
| 37L20 |
Symmetries
| 37L25 |
Inertial manifolds and other invariant attracting sets
| 37L30 |
Attractors and their dimensions, Lyapunov exponents
| 37L40 |
Invariant measures
| 37L45 |
Hyperbolicity; Lyapunov functions
| 37L50 |
Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
| 37L55 |
Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]
| 37L60 |
Lattice dynamics [See also 37K60]
[xref: 37K60]
| 37L60 |
Approximation methods (nonlinear Galerkin, etc.)
| 37L99 |
None of the above, but in this section
| |
37Mxx
| Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]
[xref: 65Pxx]
| 37M05 |
Simulation
| 37M10 |
Time series analysis
| 37M15 |
Symplectic integrators
| 37M20 |
Computational methods for bifurcation problems
| 37M25 |
Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)
| 37M99 |
None of the above, but in this section
| |
37Nxx
| Applications
| 37N05 |
Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]
| 37N10 |
Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]
| 37N15 |
Dynamical systems in solid mechanics [See mainly 74Hxx]
| 37N20 |
Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
| 37N25 |
Dynamical systems in biology [See mainly 92-XX, but also 91-XX]
| 37N30 |
Dynamical systems in numerical analysis
| 37N35 |
Dynamical systems in control
| 37N40 |
Dynamical systems in optimization and economics
| 37N99 |
None of the above, but in this section
| |