Sharkovsky ordering
E911356
Sharkovsky ordering is a specific total ordering of the natural numbers used in one-dimensional dynamical systems to characterize the coexistence and implications of periodic orbits.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Sharkovsky ordering canonical | 1 |
| Sharkovsky's theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11219432 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sharkovsky ordering Context triple: [Milnor–Thurston kneading theory, relatedTo, Sharkovsky ordering]
-
A.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
-
B.
Smale horseshoe
The Smale horseshoe is a fundamental example in dynamical systems theory that illustrates chaotic behavior through a specific stretching-and-folding map of a square into a horseshoe-shaped region.
-
C.
Denjoy–Young–Saks theorem
The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
-
D.
Poincaré–Birkhoff fixed-point theorem
The Poincaré–Birkhoff fixed-point theorem is a fundamental result in dynamical systems and topology that guarantees the existence of at least two fixed points for certain area-preserving twist maps of an annulus.
-
E.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Sharkovsky ordering Target entity description: Sharkovsky ordering is a specific total ordering of the natural numbers used in one-dimensional dynamical systems to characterize the coexistence and implications of periodic orbits.
-
A.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
-
B.
Smale horseshoe
The Smale horseshoe is a fundamental example in dynamical systems theory that illustrates chaotic behavior through a specific stretching-and-folding map of a square into a horseshoe-shaped region.
-
C.
Denjoy–Young–Saks theorem
The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
-
D.
Poincaré–Birkhoff fixed-point theorem
The Poincaré–Birkhoff fixed-point theorem is a fundamental result in dynamical systems and topology that guarantees the existence of at least two fixed points for certain area-preserving twist maps of an annulus.
-
E.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
ordering of the natural numbers ⓘ total order ⓘ |
| appearsIn |
chaos theory
ⓘ
one-dimensional real dynamics ⓘ theory of interval maps ⓘ |
| appliesTo |
continuous maps from an interval to itself
ⓘ
one-dimensional discrete-time dynamical systems ⓘ |
| basedOn | natural numbers ⓘ |
| characterizes |
period-forcing relations
ⓘ
possible sets of periods of continuous interval maps ⓘ |
| codomain | binary relation on natural numbers ⓘ |
| comparedWith |
Li–Yorke chaos
ⓘ
linked to:
chaos theory
|
| countryOfOrigin | Soviet Union ⓘ |
| definesRelationOn | set of positive integers ⓘ |
| domain | natural numbers ⓘ |
| field |
dynamical systems
ⓘ
one-dimensional dynamics ⓘ real analysis ⓘ topological dynamics ⓘ |
| hasConsequence |
existence of all periods for certain chaotic maps
ⓘ
period three implies chaos (in a stronger sense than Li–Yorke) ⓘ |
| hasNotation | "><_S" (Sharkovsky order symbol) ⓘ |
| hasProperty |
linear order
ⓘ
total order ⓘ well-defined on N ⓘ |
| implies | if a map has a periodic point of a given period, it has periodic points of all periods later in the ordering ⓘ |
| introducedBy | Oleksandr Sharkovsky ⓘ |
| introducedIn | 1964 ⓘ |
| mathematicalContext |
iteration of continuous functions
ⓘ
topological conjugacy invariants ⓘ |
| namedAfter | Oleksandr Sharkovsky ⓘ |
| originalPublicationLanguage | Russian ⓘ |
| relatedTo |
Sharkovsky's theorem
ⓘ
linked to:
Sharkovsky ordering
interval maps ⓘ logistic map ⓘ periodic points ⓘ |
| usedBy |
mathematicians studying dynamical systems
ⓘ
researchers in chaos theory ⓘ |
| usedFor |
characterizing coexistence of periodic orbits
ⓘ
describing implications between periods of periodic points ⓘ formulating Sharkovsky's theorem ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Sharkovsky ordering Description of subject: Sharkovsky ordering is a specific total ordering of the natural numbers used in one-dimensional dynamical systems to characterize the coexistence and implications of periodic orbits.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Sharkovsky ordering