Talk:Dynamical system

"Ergodic systems" section organization

Finite time solutions are an extreme opposite of ergodic behavior. Nonlinear and chaotic systems are not a subclass of ergodic systems. Finite time solutions do require nonlinearity. The organization here therefore makes very little sense. RowanElder (talk) 13:47, 29 September 2024 (UTC)

Tone

See specifically WP:PRONOUN. fgnievinski (talk) 14:00, 15 February 2026 (UTC)

let me know extra feedback if needed thx;) Flyredeagle (talk) 12:19, 20 February 2026 (UTC)

Formal definition

I feel that semi group is much more general than monoid. This current formal definition is full of bias and damaging the article.

One reason is due to the self reference. People discussed across the internet for last 12 years what the heck this formal definition means, the preceding page was deleted and the original history is not public, to prove that the guy adding the self reference was actually the guy in Cagliari.

Second reason is the community of math stack exchange attached to category theory, they don't like semi groups cause categories are typically defined top down with identity in axiomatic manner. There is a big thing with the pull back from the monoid to the semi-group, to make equality working in the extended semi-group. It is also unclear how much this category theory comes back useful as in the reference from Harvard.

Third reason semi groups are constructivist typically too where you add a different identity on the basis of need, there is a wealth of dynamical system such as finite state automata and reset mechanics that comes with multiple identities, and others with left or right identities.

Proof that this bias is damaging for example is that it was removed from the competition ... https://grokipedia.com/page/Dynamical_system}} Which ends up to be more consistent.

This difficulty is ultimately due to good Research and bogus research, and different philosophical approaches which lurks in the article.

The thing that is actually good is the measure theoretic stuff which is actually robust and sound with major theorems attached.

Finally I was listening Deutsch stating that Wikipedia is recently dying due to quality, and is unclear how it didn't die before. There's no bias, there's just error either intentional or not intentional. Flyredeagle (talk) 12:16, 20 February 2026 (UTC)

One Section Doesn't Function in Dark Mode

This is a great article. I just want to mention that some of the equations in the following section appear in white font in white background:

https://en.wikipedia.org/w/index.php?title=Dynamical_system&gesuggestededit=1#Classical_definition Starlighsky (talk) 12:55, 18 June 2026 (UTC)

reverted to 16 august 2026 version

The reasoning that the formal definiton was changed is described above and can be further discussed: the edits where done anonymously to bypass the review system, the editing parties which are related to the two citations from cagliari, they apply category theory to dynamical systems, this is traceable when the citations where initially introduced and to the revert which was done anonymously, this is quite a non standard approach and the definition is only traceable to those two links and no further academic text. The definition may be correct but is absolutely non standard and reflects the bias of the editors, the formal definiton is done with semi-groups, the same definition was moved below in the text for fairness and inclusion, it was even proposed to remove it completely given is very weird and non standard non traceable to any standard book. The academic standard recognized definition is based on semigroups. On top there are ellis semigroups, from topological dynamics which are enough of a good reason to use semigroup as the standard formal definion. In regards to the lead I will create a few extra edits to quickly improve it,

There was a wish to re-edit the lead and the full article from User:Sławomir Biały and User:Ldm1954 was involved on the draft smooth dynamics page, can you please review and agree on the revert too ? Thanks D. Flyredeagle (talk) 19:57, 2 October 2026 (UTC)

Many important points:

1. I draftified Draft:Smooth dynamics as it was written as an essay and inappropriate as written. It needs to be revised and resubmitted via AfC.
2. This was not vandalism by ~2026-45448-18. They have every right to edit and they are not bypassing anything. I am removing the tag you added as it is completely inappropriate.
3. I am dubious about some of your additions, these may be original research. I do not know enough about the details to judge.

I have posted on the talk page of ~2026-45448-18 so they know about those discussion. I am also going to post at WT:Physics and WT:MATHEMATICS so interested editors can participate in this discussion and edit the page if appropriate. Ldm1954 (talk) 01:09, 3 October 2026 (UTC)

These accounts ~2026-45448-18 are created automatically by wikipedia, when there is an anon edit, if you see the account was used only for changes to this pages, let's wait and see if they join the discussion. The feedback about non standard definition comes from User:Sławomir Biały. I also double checked multiple textbooks and secondary sources and that definition is absolutely nowhere. if you track back when it was added is many years ago and you can see is linked to the orginal authors. The definition is not per se wrong, and is due to the formalities of category theory and the inverse maps, but is totally un-natural to the extent of any teaching professor or course of dynamical systems and shall have some ground on both math and physics.

If you let me know anything in this article that can be subject of original research please let me know, so that I can either double check it or remove it. The work of Ellis semi-groups for example is from the 1970s and seems pretty well established, but I am not an academic. Flyredeagle (talk) 07:34, 3 October 2026 (UTC)