# Autocatalytic Reactions in Systems with Hyperbolic Mixing: Exact Results for the Active Baker Map

Source: [Autocatalytic Reactions in Systems with Hyperbolic Mixing: Exact Results for the Active Baker Map](<https://www.sota2.com/research/paper/68fa25802c2a3760193b0c33>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T10:45:07.282Z

Authors: Z. Toroczkai, G. Karolyi, A. Pentek, T Tel

Published: 2001-01-22T17:39:02.000Z

## Abstract

We investigate the effects of hyperbolic hydrodynamical mixing on the reaction kinetics of autocatalytic systems. Exact results are derived for the two dimensional open baker map as an underlying mixing dynamics for a two-component autocatalytic system, $A+B \\to 2B$. We prove that the hyperboliticity exponentially enhances the productivity of the reaction which is due the fact that the reaction kinetics is catalyzed by the fractal unstable manifold of the chaotic set of the reaction-free dynamics. The results are compared with phenomenological theories of active advection.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/nlin/0101040>)

[PDF](<https://arxiv.org/pdf/nlin/0101040.pdf>)