Dynamical estimates on a class of quadratic polynomial automorphisms of C-3

Quadratic automorphisms of C3 are classified up to affine conjugacy into seven classes by Fornss and Wu. Five of them contain irregular maps with interesting dynamics. In this paper, we focus on the maps in the fifth class and make some dynamical estimates for these maps.


Bivariate polynomial mappings associated with simple complex Lie algebras
Küçüksakallı, Ömer (2016-11-01)
There are three families of bivariate polynomial maps associated with the rank-2 simple complex Lie algebras A(2), B-2 congruent to C-2 and G(2). It is known that the bivariate polynomial map associated with A(2) induces a permutation of F-q(2) if and only if gcd(k, q(3) - 1) = I. for s = 1, 2, 3. In this paper, we give similar criteria for the other two families. As an application, a counterexample is given to a conjecture posed by Lidl and Wells about the generalized Schur's problem.
Invariant manifolds and Grobman-Hartman theorem for equations with degenerate operator at the derivative
Karasözen, Bülent; Loginov, B (2003-01-01)
Analog of Grobman-Hartman theorem about stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved. In contrast to usual evolution equation here central manifold arises even in the case of spectrum absence on the imaginary axis. Jordan chains tools and implicit operator theorem are used. The obtained results allow to develop center manifold methods for computation of bifurcation solution asymptotics and their stability i...
On abelian group actions with TNI-centralizers
Ercan, Gülin (2019-07-03)
A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that G is a solvable group with Fitting length h(G) is at most . In particular whenever is nonnormal. Here, h(G) is the Fitting length of G and is the number of primes dividing A counted with multiplicities.
Some conditions for a co-semigroup to be asymptotically finite-dimensional
Emelyanov, Eduard (2003-09-01)
We study the class of bounded C-0-semigroups T = (T-t)(tgreater than or equal to0) on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X-0(T) infinity)parallel toT(t)xparallel to = 0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.
Inequalities for harmonic functions on spheroids and their applications
Zahariuta, V (2001-06-01)
Hadamard-type interpolational inequalities for norms of harmonic functions are studied for confocal prolate and oblate spheroids. It is shown that the optimal level domains in such inequalities may be non-spheroidal. Moreover, in contrary with the case of analytic functions, there is an unremovable gap between the corresponding optimal level domains for inner and outer versions of Hadamard-type inequalities for harmonic functions. These results are based on some special asymptotical formulas for associated ...
Citation Formats
Ö. Yazıcı, “Dynamical estimates on a class of quadratic polynomial automorphisms of C-3,” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, pp. 230–240, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43264.