Authors
Thomas R Michel, Mathias Steinhuber, Juan Diego Urbina, Peter Schlagheck
Published in
Physical review. E. Volume 114. Issue 3-1. Pages 034213.
Abstract
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the out-of-time-ordered correlator. On the other hand, integrable dynamics near unstable fixed points, which are in turn characterized by a stability exponent, can also induce such exponential growth. Following the paradigm of integrability breaking as driven by nonlinear resonances that hallmarks the genesis of chaos, the integrability-chaos transition is universally described by a periodic perturbation applied to a generic pendulum. Remarkably, this means that within the corresponding separatrix dynamics, which is an unavoidable a consequence of the resonance scenario, both instability exponents must play a role as both dynamical regimes coexist. We report here the universality of the transition from instability to Lyapunov exponents, thus completing the resonance scenario at the level of indicators based on exponential growth. To achieve this goal we obtain an analytical expression for the time evolution near separatrices, which enables us to derive an analytical expression for the exponent that characterizes chaos and its transition from local instability to global chaos. We support our claim for the universality of this mechanism by studying two paradigmatic examples of the integrability-to-chaos transition, namely, the kicked rotor and the kicked Bose-Hubbard dimer.
PMID:
42888664
Bibliographic data and abstract were imported from PubMed on 17 Oct 2026.
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