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- Takens'_theorem abstract "In mathematics, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of a dynamical system. The reconstruction preserves the properties of the dynamical system that do not change under smooth coordinate changes, but it does not preserve the geometric shape of structures in phase space.Takens' theorem is the 1981 delay embedding theorem of Floris Takens. It provides the conditions under which a smooth attractor can be reconstructed from the observations made with a generic function. Later results replaced the smooth attractor with a set of arbitrary box counting dimension and the class of generic functions with other classes of functions.Delay embedding theorems are simpler to state fordiscrete-time dynamical systems.The state space of the dynamical system is a ν-dimensional manifold M. The dynamics is given by a smooth map Assume that the dynamics f has a strange attractor A with box counting dimension dA. Using ideas from Whitney's embedding theorem, A can be embedded in k-dimensional Euclidean space with That is, there is a diffeomorphism φ that maps A into Rk such that the derivative of φ has full rank.A delay embedding theorem uses an observation function to construct the embedding function. An observation function α must be twice-differentiable and associate a real number to any point of the attractor A. It must also be typical, so its derivative is of full rank and has no special symmetries in its components. The delay embedding theorem states that the functionis an embedding of the strange attractor A.".
- Takens'_theorem wikiPageExternalLink Attractor_Reconstruction.
- Takens'_theorem wikiPageExternalLink ChaosKit.
- Takens'_theorem wikiPageID "744335".
- Takens'_theorem wikiPageRevisionID "475232725".
- Takens'_theorem hasPhotoCollection Takens'_theorem.
- Takens'_theorem subject Category:Theorems_in_dynamical_systems.
- Takens'_theorem type Abstraction100002137.
- Takens'_theorem type Attribute100024264.
- Takens'_theorem type Communication100033020.
- Takens'_theorem type DynamicalSystem106246361.
- Takens'_theorem type DynamicalSystems.
- Takens'_theorem type Message106598915.
- Takens'_theorem type PhaseSpace100029114.
- Takens'_theorem type Proposition106750804.
- Takens'_theorem type Space100028651.
- Takens'_theorem type Statement106722453.
- Takens'_theorem type Theorem106752293.
- Takens'_theorem type TheoremsInDynamicalSystems.
- Takens'_theorem comment "In mathematics, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of a dynamical system. The reconstruction preserves the properties of the dynamical system that do not change under smooth coordinate changes, but it does not preserve the geometric shape of structures in phase space.Takens' theorem is the 1981 delay embedding theorem of Floris Takens.".
- Takens'_theorem label "Takens' theorem".
- Takens'_theorem sameAs m.037q5q.
- Takens'_theorem sameAs Q11722674.
- Takens'_theorem sameAs Q11722674.
- Takens'_theorem sameAs Takens'_theorem.
- Takens'_theorem wasDerivedFrom Takens'_theorem?oldid=475232725.
- Takens'_theorem isPrimaryTopicOf Takens'_theorem.