Piotr Migus

activity

20142026

most cited

C^{r}

-right equivalence of analytic functions

2 citations · 7 across the 9 of their papers we have counts for

collaborators

9 papers

math.AG2026

Generic degrees of real polynomial Keller maps with non-dense image

Piotr Migus

We determine the possible generic degrees of real polynomial Keller maps with non-dense image, where density is understood in the Euclidean topology. For every dimension $n \geq 3$ ,…

math.CV2026

Bi-Lipschitz invariance of Newton polygons along gradient canyons

Piotr Migus, Laurenţiu Păunescu, Mihai Tibăr

We study bi-Lipschitz right-equivalence of holomorphic function germs $f : (C^{2}, 0) \to (C, 0)$ via polar arcs and gradient canyons. For a polar arc $γ$ we consider the…

cs.LG2025★ 2 cited

Newton-Puiseux Analysis for Interpretability and Calibration of Complex-Valued Neural Networks

Piotr Migus

Complex-valued neural networks (CVNNs) are particularly suitable for handling phase-sensitive signals, including electrocardiography (ECG), radar/sonar, and wireless in-phase/quadr…

math.CV2025

On higher Lipschitz invariants

Piotr Migus, Laurenţiu Păunescu, Mihai Tibăr

We find new bi-Lipschitz invariants for functions of two complex variables.

math.CV2021★ 1 cited

Clustering polar curves

Piotr Migus, Laurenţiu Păunescu, Mihai Tibăr

This essay builds on the idea of grouping the polar curves of 2-variable function germs into polar clusters. In the topological category, one obtains a bijective correspondence bet…

math.AG2018

On quadratic polynomial mappings from the plane into the $n$ dimensional space

Michał Farnik, Zbigniew Jelonek, Piotr Migus

We show that, up to linear equivalence, there are only finitely many polynomial quadratic mappings $F : C^{2} \to C^{n}$ and $F : R^{2} \to R^{n}$ . We list all…

math.AG2015★ 1 cited

Sufficiency of non-isolated singularities

Piotr Migus, Tomasz Rodak, Stanisław Spodzieja

We give, in terms of the Łojasiewicz inequality, a sufficient condition for $C^{k}$ -mappings germs of non-isolated singularity at zero to be isotopical.

math.AG2015★ 1 cited

Local $C^{r}$ -right equivalence of $C^{r + 1}$ functions

Piotr Migus

Let $f, g : (R^{n}, 0) \to (R, 0)$ be $C^{r + 1}$ functions, $r \in N$ . We will show that if $\nabla f (0) = 0$ and there exist a neigbourhood $U$ of $0\in \ma…

math.AG2014★ 2 cited

$C^{r}$ -right equivalence of analytic functions

Piotr Migus

Let $f, g : (R^{n}, 0) \to (R, 0)$ be analytic functions. We will show that if $\nabla f (0) = 0$ and $g - f \in (f)^{r + 2}$ then $f$ and $g$ are $C^{r}$ -right equivalent…

Generic degrees of real polynomial Keller maps with non-dense image

Bi-Lipschitz invariance of Newton polygons along gradient canyons

Newton-Puiseux Analysis for Interpretability and Calibration of Complex-Valued Neural Networks

On higher Lipschitz invariants

Clustering polar curves

On quadratic polynomial mappings from the plane into the n dimensional space

Sufficiency of non-isolated singularities

Local Cr-right equivalence of Cr+1 functions

Cr-right equivalence of analytic functions

On quadratic polynomial mappings from the plane into the $n$ dimensional space

Local $C^{r}$ -right equivalence of $C^{r + 1}$ functions

$C^{r}$ -right equivalence of analytic functions