The theory of one-dimensional systems is an efficient tool in nonlinear dynamics. On the one hand, it describes one-dimensional systems fairly completely, and on the other hand exhibits all basic complicated nonlinear effects. This volume acquaints the reader with the fundamentals of the theory of one-dimensional dynamical systems. Very simple nonlinear maps with a single point of extremum, also called unimodal maps, are studied. Unimodal is found to impose hardly any restrictions on the dynamical behaviour. It also provides a view of the problems appearing in the theory of dynamical systems. and describes the methods used for their solution in the case of one-dimensional maps. The book should be of interest to researchers and postgraduate students whose work involves nonlinear dynamics.
By:
A.N. Sharkovsky, S.F. Kolyada, A.G. Sivak, V.V. Fedorenko Imprint: Springer Edition: 1997 ed. Volume: 407 Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 17mm
Weight: 1.250kg ISBN:9780792345329 ISBN 10: 0792345320 Series:Mathematics and Its Applications Pages: 262 Publication Date:30 April 1997 Audience:
College/higher education
,
Professional and scholarly
,
Professional & Vocational
,
A / AS level
,
Further / Higher Education
Format:Hardback Publisher's Status: Active
Contets.- 1. Fundamental Concepts of the Theory of Dynamical Systems. Typical Examples and Some Results.- 2. Elements of Symbolic Dynamics.- 3. Coexistence of Periodic Trajectories.- 4. Simple Dynamical Systems.- 5. Topological Dynamics of Unimodal Maps.- 6. Metric Aspects of Dynamics.- 7. Local Stability of Invariant Sets. Structural Stability of Unimodal Maps.- 8. One-Parameter Families of Unimodal Maps.- References.- Notation.