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An Alternative Approach to Generalised BV and the Application to Expanding Interval Maps
Generalised bounded variation transfer operator expanding map spectral gap
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2012/6/21
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of pie...
Asymptotic expansion of smooth interval maps
Asymptotic expansion smooth interval maps Dynamical Systems
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2012/4/16
We show that several different ways to quantify the asymptotic expansion of a non-degenerate smooth interval map coincide. A consequence is an extension to multimodal maps of the remarkable result of ...
Integrability of higher pentagram maps
Integrability of higher pentagram maps Dynamical Systems
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2012/4/23
We define higher pentagram maps on polygons in $P^d$ for any dimension $d$, which extend R.Schwartz's definition of the 2D pentagram map. We prove their integrability for both closed and twisted polyg...
Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
partial hyperbolicity singular-hyperbolicity recurrence decay of correlations local dimension hitting times
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2012/4/23
We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue...
Shrinking Targets for Countable Markov Maps
Countable Markov Maps Shrinking Targets Dynamical Systems
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2011/9/20
Abstract: Let $T$ be an expanding Markov map with a countable number of inverse branches and a repeller $\Lambda$ contained within the unit interval. Given $\alpha \in \R_+$ we consider the set of poi...
A numerical study of infinitely renormalizable area-preserving maps
renormalizable area-preserving maps numerical study Dynamical Systems
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2011/9/14
Abstract: It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equa...
Green Currents for Meromorphic Maps of Compact Kahler Manifolds
Green Currents Meromorphic Maps Compact Kahler Manifolds
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2011/9/9
Abstract: We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient co...
On stochastic stability of non-uniformly expanding interval maps
stochastic stability non-uniformly expanding interval maps Dynamical Systems
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2011/9/5
Abstract: We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under mild conditions, we prove strong stochastic sta...
Pull-back of currents by meromorphic maps
Currents Dominant meromorphic maps Intersection of currents Pullback of currents
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2011/8/31
Abstract: Let $X$ and $Y$ be compact Kahler manifolds, and let $f:X\rightarrow Y$ be a dominant meromorphic map. We define a pullback operator $f^{\sharp}$ (and its local version) for currents of the ...
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Bounded Variation Piecewise Area Preserving Maps Dynamical Systems
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2011/8/30
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
Poisson Yang-Baxter maps with binomial Lax matrices
Poisson Yang-Baxter binomial Lax matrices
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2011/7/7
A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Sklyanin brac...