Iteration Theory: Dynamical Systems and Functional Equations

DOI10.1142/S0218127403007485zbMath1056.37003OpenAlexW2026478491MaRDI QIDQ4653849

Ludwig Reich, Francisco Balibrea, Jaroslav Smítal

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127403007485

zbMATH Keywords

topological dynamicsiterative functional equationsiterative rootstopological entropyperiodic structureLi-Yorke chaosCombinatorial dynamicsminimal and omega-limit sets

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Dynamical systems involving maps of the interval (37E05) Combinatorial dynamics (types of periodic orbits) (37E15) Topological dynamics (37Bxx)

Related Items (12)

The life and mathematics of Jaroslav Smítal ⋮ On Solutions and Stability of a Functional Equation Arising from a Queueing System ⋮ CHAOS ON ONE-DIMENSIONAL COMPACT METRIC SPACES ⋮ A note on a problem on ω-limit sets ofN–dimensional skew-product maps ⋮ Strange distributionally chaotic triangular maps ⋮ The three versions of distributional chaos ⋮ Relations between distributional, Li--Yorke and \(\omega\) chaos ⋮ Strange distributionally chaotic triangular maps. II ⋮ Recent results on iteration theory: iteration groups and semigroups in the real case ⋮ Invariant scrambled sets and distributional chaos ⋮ Distributional chaos for backward shifts ⋮ Distributional chaos revisited

Cites Work

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• Typical continuous functions are not iterates
• Über eine Methode zur Auffindung stetiger Iterationen in Lie-Gruppen
• Iterations and logarithms of formal automorphisms
• Der Hauptsatz über Iteration im Ring der formalen Potenzreihen
• Roots, iterations and logarithms of formal automorphisms
• Continuous maps of the circle without periodic points
• Linearisierung formal-biholomorpher Abbildungen und Iterationsprobleme
• Dynamics in one dimension
• Über einen Satz von Shl. Sternberg in der Theorie der analytischen Iterationen
• On simultaneous Abel equations
• Enumeration, construction and random generation of block codes
• Formal power series and some theorems of J. F. Ritt in arbitrary characteristic
• A chaotic continuous map generates all probability distributions
• An index theorem for the homeomorphisms of the plane near a fixed point
• Chaos in countable dynamical system
• On a linear iterative equation
• General theory of the translation equation
• Progress of iteration theory since 1981
• Wild Cantor attractors exist
• Distributional chaos on compact metric spaces via specification properties
• Power series in one variable
• On the regularity of homeomorphisms of \(E^n\)
• Noninvertible minimal maps
• Chaotic Functions with Zero Topological Entropy
• The genesis of the notion of distributional chaos
• On Sharkovsky's cycle coexistence ordering
• Positive Sequence Topological Entropy Characterizes Chaotic Maps
• Measurable dynamics of $S$-unimodal maps of the interval
• On Devaney's Definition of Chaos
• Period Three Implies Chaos
• Multi-separation, centrifugality and centripetality imply chaos
• Scrambled sets of continuous maps of 1-dimensional polyhedra
• Dynamics of homeomorphisms on minimal sets generated by triangular mappings
• COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF
• THIRTY YEARS AFTER SHARKOVSKIĬ'S THEOREM
• On scrambled sets and a theorem of Kuratowski on independent sets
• On the Periodic Structure of Delayed Difference Equations of the Form x n = f ( x n − k ) on I and S 1
• Strange triangular maps of the square
• Fractional iteration near a fixpoint of multiplier 1.
• LOW-DIMENSIONAL COMBINATORIAL DYNAMICS
• Local Diffeomorphisms-C ∞ Realization of Formal Properties
• Orbit-closure decompositions and almost periodic properties
• Recent results on functional equations in a single variable, perspectives and open problems
• Periodic structure of \(\sigma\)-permutations maps on \(I^n\)
• Devaney's chaos or 2-scattering implies Li-Yorke's chaos

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