Related papers: Lyapunov exponents and bifurcation current for pol…
For a $C^{r}$ $(r>1)$ diffeomorphism on a compact manifold that admits a dominated splitting, this paper establishes the upper semi-continuity of the entropy map. More precisely, this paper establishes the upper semi-continuity of the…
We study the dimension spectrum of Lyapunov exponents for multimodal maps of the interval and their generalizations. We also present related results for rational maps on the Riemann sphere.
The paper provides a new integral formula for the largest Lyapunov exponent of Gaussian matrices, which is valid in the real, complex and quaternion-valued cases. This formula is applied to derive asymptotic expressions for the largest…
We study convergence of nonlinear systems in the presence of an `almost Lyapunov' function which, unlike the classical Lyapunov function, is allowed to be nondecreasing---and even increasing---on a nontrivial subset of the phase space.…
We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of Lyapunov exponents originally appearing in the theory of dynamical systems and differential…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
We study the class of functions on the set of (generalized) Young diagrams arising as the number of embeddings of bipartite graphs. We give a criterion for checking when such a function is a polynomial function on Young diagrams (in the…
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov…
We consider skew-products of quadratic maps over certain Misiurewicz-Thurston maps and study their statistical properties. We prove that, when the coupling function is a polynomial of odd degree, such a system admits two positive Lyapunov…
The Lyapunov exponents for Anderson localization are studied in a one dimensional disordered system. A random Gaussian potential with the power law decay $\sim 1/|x|^q$ of the correlation function is considered. The exponential growth of…
In this paper, we study the stability of matrix polynomials under structured perturbations of their coefficients. More precisely, we consider a family of matrix polynomials \[…
The present paper explores the spectral cocycle, defined by A. Bufetov and B. Solomyak, in the special case of bijective substitutions on two letters, the most prominent example being the Thue-Morse substitution. We derive an explicit…
Let $f:X\to X$ be a dominating meromorphic map of a compact K\"ahler surface of large topological degree. Let $S$ be a positive closed current on $X$ of bidegree $(1,1)$. We consider an ergodic measure $\nu$ of large entropy supported by…
We show that the top Lyapunov exponent $\lambda_+(p)$ , $p = (p_1, \cdots, p_N)$ with $p_i >0$ for each $i$, associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities $p$ whenever…
Let (\rho_\lambda)_{\lambda\in \Lambda} be a holomorphic family of representations of a finitely generated group G into PSL(2,C), parameterized by a complex manifold \Lambda . We define a notion of bifurcation current in this context, that…
Following the pioneering work of Iommi-Kiwi and Jenkinson-Pollicott-Vytnova, we continue to study the inflection points of the Lyapunov spectrum in this work. We prove that for any 3-branch piecewise linear expanding map on an interval, the…
We prove general mixing theorems for sequences of meromorphic maps on compact K\"ahler manifolds. We deduce that the bifurcation measure is exponentially mixing for a family of rational maps of $\mathbb{P}^q(\mathbb{C})$ endowed with…
In this paper we study polynomial maps of vector spaces and their eigenvectors and eigenvalues. The new quantity called complanart is defined. Complanarts determine complanarity of solution vectors of systems of polynomial equations.…
We prove a Liouville theorem for the plurisubharmonic functions on complete Kaelher manifolds. As the applications, we prove a splitting theorem for complete Kaehler manifolds with nonnegative biscetional curvature in terms of the linear…
We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schr\"odinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose…