Online citations, reference lists, and bibliographies.

On The Concept Of Attractor

J. Milnor
Published 1985 · Mathematics

Cite This
Download PDF
Analyze on Scholarcy
Share
This note proposes a definition for the concept of “attractor,” based on the probable asymptotic behavior of orbits. The definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor.



This paper is referenced by
10.1016/J.CHAOS.2015.07.011
Evolutionary Competition between Boundedly Rational Behavioral Rules in Oligopoly Games
Lorenzo Cerboni Baiardi (2015)
10.1103/PhysRevD.101.024025
Stable attractors in the three-dimensional general relativistic Poynting-Robertson effect.
Vittorio De Falco (2019)
Chaotic Itinerancy in Regional Business Cycle Synchronization
T. Onozaki (2015)
10.1063/1.1586531
Phase resetting effects for robust cycles between chaotic sets.
P. Ashwin (2003)
10.1016/S0167-2789(02)00623-1
Symmetry restoration in a class of forced oscillators
A. Ben-Tal (2002)
10.1007/978-94-017-0470-0_6
History of Shape Theory and its Application to General Topology
S. Mardešić (2001)
10.1016/S0898-1221(98)80038-2
Attractors of continuous difference equations
E. Romanenko (1998)
10.1007/978-3-319-57771-5_2
Definitions and Major Assumptions
Glenn D. Walters (2017)
10.1007/978-3-030-37530-0_1
Phase Space in Chaos and Nonlinear Dynamics
Tuan Pham (2020)
10.1063/1.2965524
Random parameter-switching synthesis of a class of hyperbolic attractors.
Marius-F. Danca (2008)
10.1090/S0002-9947-2012-05644-3
On the existence of attractors
C. Bonatti (2009)
10.1007/978-94-010-0217-2_4
Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems
K. Kaneko (2003)
10.1007/S11072-005-0007-9
Stability of synchronized and clustered states in a system of coupled piecewise-linear maps
I. Matskiv (2004)
10.1088/0951-7715/19/9/001
How chaotic are strange non-chaotic attractors?
P. Glendinning (2006)
10.1007/S11071-011-0172-6
Finding attractors of continuous-time systems by parameter switching
Marius-F. Danca (2011)
10.1088/0951-7715/11/2/007
Unique ergodicity and the approximation of attractors and their invariant measures using Ulam's method
Fern Y. Hunt (1998)
10.1016/S0167-2789(97)80006-1
On the unfolding of a blowout bifurcation
P. Ashwin (1998)
Old and Young. Can they coexist
N. Davydova (2004)
Attractors on $\mathbf{P}^k$
F. Rong (2005)
10.1007/978-94-010-0217-2_6
Synchronization and Clustering in Ensembles of Coupled Chaotic Oscillators
Y. Maistrenko (2003)
10.1088/0951-7715/15/3/306
Riddling and invariance for discontinuous maps preserving Lebesgue measure
P. Ashwin (2002)
10.11606/T.3.2009.TDE-08092010-121108
M3DS: um modelo de dinâmica de desenvolvimento distribuído de software.
A. L'Erário (2009)
10.1007/S10955-013-0903-9
Breaking of Ergodicity in Expanding Systems of Globally Coupled Piecewise Affine Circle Maps
B. Fernandez (2014)
10.1063/1.4892530
How well-connected is the surface of the global ocean?
G. Froyland (2014)
10.1016/J.CHAOS.2012.01.009
The discontinuous flat top tent map and the nested period incrementing bifurcation structure
Ben W. Futter (2012)
10.1017/S0143385712000375
Strange non-chaotic attractors in quasiperiodically forced circle maps: Diophantine forcing
Tobias Jäger (2011)
10.1016/j.matcom.2013.09.007
Oligopoly model with recurrent renewal of capital revisited
Anastasiia Panchuk (2015)
10.1007/978-3-319-12805-4_10
Dynamics of Industrial Oligopoly Market Involving Capacity Limits and Recurrent Investment
Anastasiia Panchuk (2015)
10.1007/978-3-319-96755-4_3
Applying Circulant Matrices Properties to Synchronization Problems
Jose S. Cánovas (2019)
10.1017/JFM.2014.601
Nonlinear Self-Excited Thermoacoustic Oscillations of a Ducted Premixed Flame: Bifurcations and Routes to Chaos
K. Kashinath (2013)
10.1109/SASO.2007.54
Self-organizing Replica Placement - A Case Study on Emergence
K. Herrmann (2007)
10.4007/ANNALS.2006.163.383
Decay of geometry for unimodal maps: An elementary proof
W. Shen (2006)
See more
Semantic Scholar Logo Some data provided by SemanticScholar