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

This page provides a list of all articles available at PlanetMath in the following topic:

37-XX Dynamical systems and ergodic theory.

This list will be periodically updated. Each entry in the list has three fields:

1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:

Status	means PM article
N	not needed
A	adequately covered
C	copied
M	merged
NC	needs copying
NM	needs merging

• Please update the WP and Status fields as appropriate.
• if the WP field is correct please remove the qualifier "guess".
• If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
• If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
• If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

• {{planetmath|id=|title=}} for copied over text
• {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

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)