A first course in discrete dynamical systems

zbMath0797.58001MaRDI QIDQ1324694

R. A. Holmgren

Publication date: 26 May 1994

Published in: Universitext (Search for Journal in Brave)

zbMATH Keywords

chaosNewton's methodJulia setsbifurcationssymbolic dynamicsdiscrete dynamical systemsstable setslogistic functioniterated functionsperiodical pointsSharkovskij's theoremMandelbrot setsparametrized families of functions

Mathematics Subject Classification ID

Topological dynamics (37B99) Discrete version of topics in analysis (39A12) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis (58-01) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

A new discrete dynamical system of signed integer partitions, Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game, RELATION BETWEEN KNEADING MATRICES OF A MAP AND ITS ITERATES, Bifurcating neuron: Computation and learning, Fractional-order Chua's system: discretization, bifurcation and chaos, On the dynamics of a discrete difference map in Mann orbit, Topologically transitive and mixing properties of set-valued dynamical systems, Chaos in hyperspaces of nonautonomous discrete systems, Necessary conditions for extended spectral decomposable multivalued linear operators, Bifurcation and global stability of a discrete prey–predator model with saturated prey refuge, A new iterative approach to fractal models, The application of Newton's method in vector form for solving nonlinear scalar equations where the classical Newton method fails, Dynamics of Discrete Operator Equations, On a discretization process of fractional-order logistic differential equation, Stability of real parametric polynomial discrete dynamical systems, A Novel Fixed Point Feedback Approach Studying the Dynamical Behaviors of Standard Logistic Map, INVARIANCE OF KNEADING MATRIX UNDER CONJUGACY, Dynamics of the iteration operator on the space of continuous self-maps, Discrete dynamics of one dimensional Collatz like integral value transformations, Uniform convergence and transitivity, Bounds on the Hausdorff dimension of a renormalisation map arising from an excitable reaction-diffusion system on a fractal lattice, Iterated linear optimization, Evolution of specialization under non-equilibrium population dynamics, The `Butterfly effect' in Cayley graphs with applications to genomics., Applications of Fixed Point Theorems in Divisibility of Polynomials, A novel four-step feedback procedure for rapid control of chaotic behavior of the logistic map and unstable traffic on the road, On bifurcation and chaos in a discrete dynamical system, Discrete Chaotification of a Modulated Logistic System, Julia sets of certain exponential functions, Dynamics of a family of orbitally continuous mappings