Wiki143:WikiProject Mathematics/PlanetMath Exchange/37-XX Dynamical systems and ergodic theory

37-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: no-cycles condition, id=6054 -- WP guess: no-cycles condition -- Status:

• PM: symbolic dynamics, id=8639^new! -- WP guess: symbolic dynamics -- Status:

37A05 Measure-preserving transformations

• PM: Poincaré recurrence theorem, id=6033 -- WP: Poincaré recurrence theorem -- Status: M

linas 14:54, 6 June 2006 (UTC)

• PM: proof of Poincaré recurrence theorem 1, id=6035 -- WP: Poincaré recurrence theorem -- Status: N

Its a proof, marking as "not needed". linas 14:54, 6 June 2006 (UTC)

• PM: proof of Poincaré recurrence theorem 2, id=6036 -- WP: Poincaré recurrence theorem -- Status: N

Its a proof, marking as "not needed". linas 14:54, 6 June 2006 (UTC)

37A25 Ergodicity, mixing, rates of mixing

• PM: mixing, id=5511 -- WP: strong mixing -- Status: A

linas 04:23, 5 September 2005 (UTC)

37A30 Ergodic theorems, spectral theory, Markov operators

• PM: ergodic, id=1949 -- WP: ergodic (adjective) -- Status: C

linas 23:26, 6 June 2006 (UTC)

• PM: ergodic theorem, id=1996 -- WP: ergodic theorem -- Status: M

linas 00:16, 7 June 2006 (UTC)

• PM: example of fundamental theorem of demography, id=5716 -- WP: fundamental theorem of demography -- Status: NC

linas 18:56, 10 June 2006 (UTC)

• PM: fundamental theorem of demography, id=3813 -- WP: fundamental theorem of demography -- Status: NC

linas 18:56, 10 June 2006 (UTC)

• PM: proof of fundamental theorem of demography, id=3957 -- WP guess: proof of fundamental theorem of demography -- Status: N

Its a proof,, not needed as per current policy. linas 00:30, 7 June 2006 (UTC)

37B05 Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• PM: discontinuous action, id=4051 -- WP: discontinuous action -- Status: M

linas 00:20, 7 June 2006 (UTC)

• PM: properly discontinuous action, id=4039 -- WP: properly discontinuous action -- Status: A

linas 04:00, 7 June 2006 (UTC)

37B20 Notions of recurrence

• PM: nonwandering set, id=4314 -- WP: nonwandering set -- Status: A

linas 00:28, 7 June 2006 (UTC)

• PM: recurrent point, id=6034 -- WP: recurrent point -- Status: C

linas 00:28, 7 June 2006 (UTC)

37B35 Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets

• PM: locally maximal, id=5530 -- WP guess: locally maximal -- Status:

37B40 Topological entropy

• PM: topological entropy, id=6068 -- WP: topological entropy -- Status: C

linas 14:14, 7 June 2006 (UTC)

37B99 Miscellaneous

• PM: \omega-limit set, id=4316 -- WP: limit set -- Status: C

linas 14:43, 9 June 2006 (UTC)

• PM: asymptotically stable, id=4679 -- WP: Lyapunov stable -- Status: M

linas 15:40, 8 June 2006 (UTC)

• PM: expansive, id=4513 -- WP: expansive -- Status: C

linas 19:27, 10 June 2006 (UTC)

• PM: the only compact metric spaces that admit a positively expansive homeomorphism are discrete spaces, id=4677 -- WP: positively expansive -- Status: N

Its a proof, noew referenced in article on expansive. linas 19:27, 10 June 2006 (UTC)

• PM: topological conjugation, id=4353 -- WP: topological conjugation -- Status: C

linas 16:06, 10 June 2006 (UTC)

• PM: topologically transitive, id=4354 -- WP: topologically transitive -- Status: A

linas 14:57, 7 June 2006 (UTC)

• PM: uniform expansivity, id=4678 -- WP: uniform expansivity -- Status: C

linas 19:52, 10 June 2006 (UTC)

37C05 Smooth mappings and diffeomorphisms

• PM: Hayashi's connecting lemma, id=5527 -- WP guess: Hayashi's connecting lemma -- Status:

37C10 Vector fields, flows, ordinary differential equations

• PM: flow, id=3673 -- WP: flow (mathematics) -- Status: C

linas 15:09, 5 September 2005 (UTC)

• PM: Frobenius' theorem, id=6543 -- WP: Frobenius theorem (differential topology) -- Status: A

linas 17:15, 5 September 2005 (UTC)

• PM: globally attracting fixed point, id=3534 -- WP: globally attracting fixed point -- Status: N

PM article appears to have been retired/obsoleted (I get a permissions error on view). linas 20:22, 10 June 2006 (UTC)

• PM: integral manifold, id=6542 -- WP: integral manifold -- Status: A

linas 17:04, 5 September 2005 (UTC)

37C20 Generic properties, structural stability

• PM: Kupka-Smale theorem, id=4360 -- WP guess: Kupka-Smale theorem -- Status:

• PM: Pugh's closing lemma, id=5526 -- WP guess: Pugh's closing lemma -- Status:

• PM: Pugh's general density theorem, id=4345 -- WP guess: Pugh's general density theorem -- Status:

37C25 Fixed points, periodic points, fixed-point index theory

• PM: Hartman-Grobman theorem, id=5928 -- WP guess: Hartman-Grobman theorem -- Status:

• PM: hyperbolic fixed point, id=4516 -- WP: hyperbolic fixed point -- Status: M

linas 01:04, 8 June 2006 (UTC)

• PM: proof of Hartman-Grobman theorem, id=5933 -- WP: Hartman-Grobman theorem -- Status: N

Its a proof, which we don't copy into WP as a matter of current policy. linas 01:27, 8 June 2006 (UTC)

37C29 Homoclinic and heteroclinic orbits

• PM: heteroclinic, id=4533 -- WP: heteroclinic -- Status: A

linas 14:54, 7 June 2006 (UTC)

• PM: homoclinic, id=4532 -- WP: homoclinic -- Status: A

linas 14:54, 7 June 2006 (UTC)

• PM: homoclinic class, id=5532 -- WP: homoclinic class -- Status: NC

linas 14:54, 7 June 2006 (UTC)

37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.)

• PM: pseudo-orbit, id=5528 -- WP: pseudo-orbit -- Status: NC

linas 20:19, 10 June 2006 (UTC)

• PM: shadowing lemma, id=5529 -- WP: shadowing lemma -- Status: NC

linas 01:27, 8 June 2006 (UTC)

37C70 Attractors and repellers, topological structure

• PM: unstable fixed point, id=3538 -- WP: unstable fixed point -- Status: A

linas 01:23, 8 June 2006 (UTC)

37C75 Stability theory

• PM: \Omega-stability theorem, id=6055 -- WP guess: \Omega-stability theorem -- Status:

• PM: attracting fixed point, id=3533 -- WP: attracting fixed point -- Status: A

linas 14:55, 7 June 2006 (UTC)

• PM: stable manifold, id=4357 -- WP: stable manifold -- Status: C

linas 14:55, 7 June 2006 (UTC)

37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

• PM: Anosov diffeomorphism, id=4511 -- WP: Anosov diffeomorphism -- Status: M

Merged by Charles Matthews on 27 July 2005 linas 14:50, 5 September 2005 (UTC)

• PM: Axiom A, id=4340 -- WP: Axiom A -- Status: C

linas 00:37, 8 June 2006 (UTC)

• PM: hyperbolic set, id=4338 -- WP: hyperbolic set -- Status: C

linas 04:24, 11 September 2005 (UTC)

• PM: Smale's spectral decomposition theorem, id=5990 -- WP guess: Smale's spectral decomposition theorem -- Status:

37D99 Miscellaneous

• PM: Kupka-Smale, id=4359 -- WP guess: Kupka-Smale -- Status:

37E05 Maps of the interval (piecewise continuous, continuous, smooth)

• PM: Sharkovskii's theorem, id=3751 -- WP: Sharkovskii's theorem -- Status: A

linas 19:48, 7 June 2006 (UTC)

37E30 Homeomorphisms and diffeomorphisms of planes and surfaces

• PM: Alexander trick, id=7895^new! -- WP guess: Alexander trick -- Status:

37G15 Bifurcations of limit cycles and periodic orbits

• PM: Feigenbaum constant, id=2822 -- WP: Feigenbaum constant -- Status: NM

linas 14:54, 5 September 2005 (UTC)

• PM: Feigenbaum fractal, id=2820 -- WP: Feigenbaum fractal -- Status: A

linas 04:08, 8 June 2006 (UTC)

37G40 Symmetries, equivariant bifurcation theory

• PM: bifurcation problem with symmetry group, id=4639 -- WP guess: bifurcation problem with symmetry group -- Status:

• PM: Poénaru (1976) theorem, id=4352 -- WP guess: Poénaru theorem -- Status:

• PM: trace formula, id=4431 -- WP: trace formula -- Status: N

I don't think the PM article is good enough to copy. There are many trace formulas, this is a "minor" one; also, its only correct for the fundamental rep, I believe. So 'N for now. linas 03:09, 8 June 2006 (UTC)

37G99 Miscellaneous

• PM: chaotic dynamical system, id=3507 -- WP: chaotic dynamical system -- Status: A

linas 00:39, 8 June 2006 (UTC)