Possible Occurrence of Hyperbolic Attractors

作者: Sergey P Kuznetsov , Sergey P Kuznetsov

DOI: 10.1007/978-3-642-23666-2_2

关键词: Weierstrass functionLorenz systemDynamical systems theoryApplied mathematicsDifferential equationMathematicsAttractorLyapunov exponentComputationDegree (graph theory)

摘要: In this chapter we review some situations considered or mentioned in literature that may have relation to occurrence of uniformly hyperbolic attractors dynamical systems represented by maps differential equations. To date, the approaches under discussion are developed different extents. Only few them elaborated up such degree allow illustrating on a level numerical computations. Nevertheless, collected material is undoubted significance for prospects search real-world with design physical and technical devices operating due presence attractors.

参考文章(36)
Edward Ott, Chaos in Dynamical Systems Cambridge University Press. ,(2002) , 10.1017/CBO9780511803260
David K. Arrowsmith, C. M. Place, An Introduction to Dynamical Systems ,(1990)
Arthur Oscar Lopes, An example of polynomial interpolation of an hyperbolic attractor Springer Berlin Heidelberg. pp. 498- 511 ,(1983) , 10.1007/BFB0061431
C.A. Morales, Lorenz attractor through saddle-node bifurcations Annales De L Institut Henri Poincare-analyse Non Lineaire. ,vol. 13, pp. 589- 617 ,(1996) , 10.1016/S0294-1449(16)30116-0
Heinz Georg Schuster, Deterministic chaos: An introduction ,(1984)
VLADIMIR BELYKH, IGOR BELYKH, ERIK MOSEKILDE, HYPERBOLIC PLYKIN ATTRACTOR CAN EXIST IN NEURON MODELS International Journal of Bifurcation and Chaos. ,vol. 15, pp. 3567- 3578 ,(2005) , 10.1142/S0218127405014222