A New Route to Chaos through the Geometric Composition of Non-Normal Amplification
D. Sornette, V. R. Saiprasad, V. Troude
Abstract
Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate hL over L successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.
Create a lesson
Related papers
Dynamics, periodic orbits and C1 non-integrability of the ABC flow
Wojciech Szumiński, Jaume Llibre
Requirement-Induced Predictive Geometry for Finite-Resource Prediction in Dynamical Systems
Song-Ju Kim
Decision-Related Cognitive Signatures from Fast-Slow Dynamics: A Low-Dimensional Observation-Operator Framework
Furkan Emre Isik, Ali Demirci
A Canonical Lagrangian Formulation of the Two-Dimensional Lotka-Volterra System
Dima Watkins, Gene Chen
Integrable and Chaotic 4-Dimensional Lotka-Volterra Models and Population Sustainability
H. Christodoulidi, T. E. Kouloukas, L. B. Drossos et al.
First-order integrability-breaking phase transitions in dynamical systems
Anne Ketri P. da Fonseca, Marcelo de Almeida Presotto, Diego F. M. Oliveira et al.