Computation of the \L ojasiewicz exponents of real bivariate analytic functions

TL;DR

This paper provides explicit formulas for calculating the Łojasiewicz exponent, which measures the growth rate comparison between two real bivariate analytic functions, aiding in understanding their local behavior.

Contribution

It introduces new explicit formulas for the Łojasiewicz exponent in the context of real bivariate analytic functions, enhancing computational methods.

Findings

Derived explicit formulas for Łojasiewicz exponents

Improved understanding of growth rate comparisons

Facilitated calculations for real bivariate functions

Abstract

The main goal of this paper is to present some explicit formulas for computing the {{\L}}ojasiewicz exponent in the {{\L}}ojasiewicz inequality comparing the rate of growth of two real bivariate analytic function germs.