Statistical properties of a dissipative kicked system: critical exponents and scaling invariance

TL;DR

This paper introduces a universal empirical function based on a critical exponent to describe the scaling behavior in a dissipative kicked rotator, covering regimes of strong and weak dissipation and revealing a phase transition in action growth.

Contribution

It proposes a new universal empirical function dependent on a single critical exponent to model scaling in dissipative kicked systems, including phase transition behavior.

Findings

Feigenbaum constant calculated for period doubling route to chaos.

Universal empirical function accurately describes phase transition in action growth.

Scaling formalism applies to both strong and weak dissipation regimes.

Abstract

A new universal {\it empirical} function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal {\it empirical} function describes remarkably well a phase transition from limited to unlimited growth of the average action.