Preprint Article Version 1 This version is not peer-reviewed

Orbits Connectivity and the False Asymptotic Behavior at Iterated Functions with Lyapunov Stability

Version 1 : Received: 6 September 2019 / Approved: 8 September 2019 / Online: 8 September 2019 (16:09:07 CEST)
Version 2 : Received: 16 September 2019 / Approved: 17 September 2019 / Online: 17 September 2019 (04:53:25 CEST)

How to cite: Roberto Telles, C. Orbits Connectivity and the False Asymptotic Behavior at Iterated Functions with Lyapunov Stability. Preprints 2019, 2019090086 (doi: 10.20944/preprints201909.0086.v1). Roberto Telles, C. Orbits Connectivity and the False Asymptotic Behavior at Iterated Functions with Lyapunov Stability. Preprints 2019, 2019090086 (doi: 10.20944/preprints201909.0086.v1).

Abstract

By defining a constant probabilistic orbit of and iterated functions, the stability dynamics of these functions in possible interactions through connectivity provides the formation of a dynamic fixed point as a metric space between both iterated functions. The presence of a dynamic fixed point identifies qualitatively phases of iteration time lengths and interaction orbits of the event. Qualitative results show that the greater the average distance from one of the functions to the fixed point of the other (all possible solutions), the higher the iteration expression on time (false asymptotic effect) of one of the functions and in the opposite hand, the lower the average distance, the higher orbit’s interactions proximity between iterated functions (stability). This feature reveals asymptotic (well-defined) behavior between functions f and g within a well-defined Lyapunov stability.

Subject Areas

iterated function; asymptotic analysis; discretization; stability theory; metric space; qualitative theory of differential equations

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