The Importance of the Strategy in Backward Orbits

TL;DR

This paper explores the behavior of chaotic dynamical systems when their orbits are traced backwards, revealing that backward orbits are highly sensitive to the chosen strategy and highlighting the unpredictability of past states.

Contribution

It introduces the concept of a strategy parameter in backward orbits, showing its influence on the asymptotic behavior of reversed chaotic trajectories.

Findings

Backward orbits depend critically on the strategy used.

Reversed dynamics uncover new parameters affecting orbit behavior.

Backward trajectories demonstrate increased sensitivity and unpredictability.

Abstract

This work considers reversed evolution in dynamical systems. In particular, asymptotic behavior of chaotic systems, when their orbits evolve backwards in time. Reversed dynamics reveals important aspects of the trajectories, such as a new necessary parameter. This is the strategy through which one orbit reaches an original state in the past. As a result, it is found that backward orbits exhibit sensitivity to the strategy. This gives additional evidence about the unpredictability of the past