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.
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 NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| introducedIn | 1964 ⓘ |
| mathematicalContext |
iteration of continuous functions
ⓘ
topological conjugacy invariants ⓘ |
| namedAfter | Oleksandr Sharkovsky NERFINISHED ⓘ |
| originalPublicationLanguage | Russian ⓘ |
| relatedTo |
Sharkovsky's theorem
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.