@misc{10481/91912,
year = {2023},
month = {11},
url = {https://hdl.handle.net/10481/91912},
abstract = {Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific
initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase
space otherwise displaying unusual behavior. Yet, finding such initial conditions is a daunting task
precisely because of the chaotic nature of the system. In this Letter, we circumvent this problem by
proposing a framework for finding an effective topologically conjugate map whose typical trajectories
correspond to atypical ones of the original map. This is illustrated by means of examples which focus on
counterbalancing the instability of fixed points and periodic orbits, as well as on the characterization of a
dynamical phase transition involving the finite-time Lyapunov exponent. The procedure parallels that of the
application of the generalized Doob transform in the stochastic dynamics of Markov chains, diffusive
processes, and open quantum systems, which in each case results in a new process having the prescribed
statistics in its stationary state. This Letter thus brings chaotic maps into the growing family of systems
whose rare fluctuations—sustaining prescribed statistics of dynamical observables—can be characterized
and controlled by means of a large-deviation formalism.},
organization = {Ministerio de Ciencia e Innovación (Spain), by Agencia Estatal de Investigación (AEI, Spain, 10.13039/501100011033), and by European Regional Development Fund (ERDF, A way of making Europe), through Grants No. PID2020–113681 GB-I00, No. PID2021-128970OAI00, and No. PID2021-123969NB-I00},
organization = {Junta de Andalucía (Spain)-Consejería de Economía y Conocimiento 2014-2020 through Grant No. A-FQM-644-UGR20},
organization = {Comunidad de Madrid (Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), in the context of the V Plan Regional de Investigación Científica e Innovación Tecnológica (PRICIT)},
publisher = {American Physical Society},
title = {Finding the Effective Dynamics to Make Rare Events Typical in Chaotic Maps},
doi = {10.1103/PhysRevLett.131.227201},
author = {Gutiérrez, Ricardo and Canella Ortiz, Adrián and Pérez Espigares, Carlos},
}