3 citations · 17 across the 16 of their papers we have counts for
17 papers
Order and Pascal depth of Pascal finite automorphisms of the plane
Elżbieta Adamus, Zbigniew Hajto
Let be a field of characteristic . For a Pascal finite automorphism of the affine plane we show that its order is determined by its Pascal depth, $|F|=p^{\lceil\log_pτ…
On the Jung-van der Kulk decomposition into Pascal finite factors
Elżbieta Adamus, Zbigniew Hajto
Combining the Jung--van der Kulk theorem with the conjugacy invariance of the Pascal finite class, we show that every polynomial automorphism of the plane over an arbitrary fie…
Strongly nilpotent automorphisms are Pascal finite
Elżbieta Adamus, Zbigniew Hajto
We compare two classes of polynomial automorphisms, strongly nilpotent and Pascal finite. We conclude that every strongly nilpotent automorphism is a Pascal finite one, but not vic…
Real Liouvillian Extensions of Partial Differential Fields
Teresa Crespo, Zbigniew Hajto, Rouzbeh Mohseni
In this paper, we establish Galois theory for partial differential systems defined over formally real differential fields with a real closed field of constants and over formally $p…
Tame topology and non-integrability of dynamical systems
Zbigniew Hajto, Rouzbeh Mohseni
In this paper we study the general concept of integrability in the broad sense within the frame of differential Galois theory. We concentrate on the gradient systems which are not…
Jacobian Conjecture via Differential Galois Theory
Elzbieta Adamus, Teresa Crespo, Zbigniew Hajto
We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking t…
On some nice polynomial automorphisms
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
Given a polynomial endomorphism F of the n-dimensional affine space over a field K, we define a sequence of polynomial endomorphisms of the affine space associated to F. We call F…
A new characterization of the invertibility of polynomial maps
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of p…
Jacobian Conjecture and Nilpotency
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
For K a field of characteristic 0 and d any integer number greater than or equal to 2, we prove the invertibility of polynomial endomorphisms of the affine space of dimension d ove…
An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
Elzbieta Adamus, Pawel Bogdan, Zbigniew Hajto
In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions. Our theorem completes the earlier work of T.…
An inversion algorithm for polynomial maps
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polyn…
Galois correspondence theorem for Picard-Vessiot extensions
Teresa Crespo, Zbigniew Hajto, Elzbieta Sowa-Adamus
In this paper, we generalize the definition of the differential Galois group and the Galois correspondence theorem established previously for Picard-Vessiot extensions of real diff…
Picard-Vessiot Extensions of Real Differential Fields
Teresa Crespo, Zbigniew Hajto
For a linear differential equation defined over a formally real differential field K with real closed field of constants k, Crespo, Hajto and van der Put proved that there exists a…
Real and p-adic Picard-Vessiot fields
Teresa Crespo, Zbigniew Hajto, Marius van der Put
We consider differential modules over real and p-adic differential fields such that their field of constants is real closed (respectively p-adically closed). Using Deligne's work o…
The unicity of real Picard-Vessiot fields
Teresa Crespo, Zbigniew Hajto, Marius van der Put
The unicity of real Picard-Vessiot fields for differential modules over a real differential field is proved.
Picard-Vessiot theory for real partial differential fields
Teresa Crespo, Zbigniew Hajto
We prove the existence of real Picard-Vessiot extensions for real partial differential fields with real closed field of constants. We establish a Galois correspondence theorem for…
Real Picard-Vessiot theory
Teresa Crespo, Zbigniew Hajto, Elzbieta Sowa
The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has a…