Related papers: Structural Instability of Semi-Siegel H\'enon maps
We study the dynamics of the H\'enon map defined over complete, locally compact non-Archimedean fields of odd residue characteristic. We establish basic properties of its one-sided and two-sided filled Julia sets, and we determine, for each…
We study stability and bifurcations in holomorphic families of polynomial automorphisms of C^2. We say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there. We first show that this defines…
We develop a renormalization theory of non-perturbative dissipative H\'enon-like maps with combinatorics of bounded type. The main novelty of our approach is the incorporation of Pesin theoretic ideas to the renormalization method, which…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
Dynamical systems whose symplectic structure degenerates, becoming noninvertible at some points along the orbits are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the…
We study the dynamics of two conservatively coupled H\'enon maps at different levels of dissipation. It is shown that the decrease of dissipation leads to changes in the parameter plane structure and scenarios of transition to chaos…
Considering random noise in finite dimensional parameterized families of diffeomorphisms of a compact finite dimensional boundaryless manifold M, we show the existence of time averages for almost every orbit of each point of M, imposing…
A well-known theorem due to Ma\~n\'e-Sad-Sullivan and Lyubich asserts that J-stable maps are dense in any holomorphic family of rational maps in dimension 1. In this paper we show that the corresponding result fails in higher dimension.…
In this paper, we study rigidity of polynomials of arbitrary degree in the presence of neutral dynamics. Specifically, we focus on {non-renormalizable} (in the sense of Douady and Hubbard) complex polynomials of degree $d \geqslant 2$ that…
This is a continuation of the study of the theory of quantum stochastic dilation of completely positive semigroups on a von Neumann or $C^*$ algebra, here with unbounded generators. The additional assumption of symmetry with respect to a…
In the family of area-contracting H\'enon-like maps with zero topological entropy we show that there are maps with infinitely many moduli of stability. Thus one cannot find all the possible topological types for non-chaotic area-contracting…
Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong…
We investigate the random dynamics of polynomial maps on the Riemann sphere and the dynamics of semigroups of polynomial maps on the Riemann sphere. In particular, the dynamics of a semigroup $G$ of polynomials whose planar postcritical set…
Non-renormalizable Newton maps are rigid. More precisely, we prove that their Julia set carries no invariant line fields and that the topological conjugacy is equivalent to quasi-conformal conjugacy in this case.
In this paper, we prove that escaping set of transcendental semigroup is S-forward invariant. We also prove that if holomorphic semigroup is abelian, then Fatou set, Julia set and escaping set are S-completely invariant. We see certain…
The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…
Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following $C^{\ast}$-algebraic setting: A given hermitian dissipative mapping $\delta$ is…
Assume $G$ is a definable group in a stable structure $M$. Newelski showed that the semigroup $S_G(M)$ of complete types concentrated on $G$ is an inverse limit of the $\infty$-definable (in $M^{eq}$) semigroups $S_{G,\Delta}(M)$. He also…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. Moreover, we investigate the associated random dynamics of polynomials.…