37-XX
|
Dynamical systems and ergodic theory
[See also
26A18,
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
|
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
|
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]
|
37B05
|
Transformations and group actions with special properties (minimality, distality, proximality, etc.)
|
37B10
|
Symbolic dynamics
[See also
37Cxx,
37Dxx]
|
37B15
|
Cellular automata
|
37B20
|
Notions of recurrence
|
37B25
|
Lyapunov functions and stability; attractors, 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
|
37B99
|
None of the above, but in this section
|
37Cxx
|
Smooth dynamical systems: general theory
[See also
34Cxx,
34Dxx]
|
37C05
|
Smooth mappings and diffeomorphisms
|
37C10
|
Vector fields, flows, ordinary differential equations
|
37C15
|
Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
|
37C20
|
Generic properties, structural stability
|
37C25
|
Fixed points, periodic points, fixed-point index theory
|
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
37B50]
|
37C65
|
Monotone flows
|
37C70
|
Attractors and repellers, topological structure
|
37C75
|
Stability theory
|
37C80
|
Symmetries, equivariant dynamical systems
|
37C85
|
Dynamics of group actions other than Z and R, and foliations
[See mainly
22Fxx]
|
37C99
|
None of the above, but in this section
|
37Dxx
|
Dynamical systems with hyperbolic behavior
|
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
|
37D50
|
Hyperbolic systems with singularities (billiards, etc.)
|
37D99
|
None of the above, but in this section
|
37Exx
|
Low-dimensional dynamical systems
|
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
|
Homeomorphism and diffeomorphisms of plane 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]
|
37F05
|
Relations and correspondences
|
37F10
|
Polynomials; rational maps; entire and meromorphic functions
|
37F15
|
Expanding maps; hyperbolicity; structural stability
|
37F20
|
Combinatorics and topology
|
37F25
|
Renormalization
|
37F30
|
Quasiconformal methods and Teichm\"uller 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
|
37F99
|
None of the above, but in this section
|
37Gxx
|
Local and global bifurcation theory
|
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
|
37G35
|
Attractors and their bifurcations arising in bifurcations
|
37G40
|
Symmetries, equivariant bifurcation theory
|
37G99
|
None of the above, but in this section
|
37Hxx
|
Random dynamical systems
|
37H05
|
Foundations, general theory of cocycles, algebraic ergodic theory
[See also
37Axx]
|
37H10
|
Generation, random and stochastic difference and differential equations
[See also
34K50,
37F05,
60Hxx]
|
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,
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
|
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 for Lagrangian systems
|
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]
|
37K05
|
Hamiltonian structures, symmetries, variational principles, conservation laws
|
37K10
|
Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
|
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 - B\"acklund and other transformations
|
37K40
|
Soliton theory, asymptotic behavior of solutions
|
37K45
|
Stability problems
|
37K50
|
Bifurcation problems
|
37K55
|
Perturbations, KAM for infinite-dimensional systems
|
37K60
|
Lattice dynamics
[See also
37L60]
|
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]
|
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
|
37L60
|
Lattice dynamics
[See also
37K60]
|
37L65
|
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]
|
37M05
|
Simulation
|
37M10
|
Time series analysis
|
37M15
|
Symplectic integrators
|
37M20
|
Computation of homoclinic cycles
|
37M25
|
Computational methods for bifurcation problems
|
37M30
|
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 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
|