57 citations · 320 across the 46 of their papers we have counts for
56 papers
Nonuniform dichotomies via time rescaling
Davor Dragicevic, Cesar M. Silva
We establish characterizations of general nonuniform dichotomies for linear nonautonomous dynamical systems in terms of nonuniform exponential dichotomies of appropriately time-res…
Shadowing and Topological Stability via Generalized Pseudo-Hyperbolicity in Autonomous and Nonautonomous Linear Dynamics
Davor Dragicevic, Mihaly Pituk
Although generalized hyperbolicity has proved to be a fundamental notion in linear dynamics, recent results show that it is too restrictive to characterize the shadowing property o…
Smooth linearization of nonautonomous dynamics under general dichotomic behaviour
Lucas Backes, Davor Dragicevic, Wenmeng Zhang
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linea…
Quenched and annealed linear response for some partially hyperbolic skew products
Davor Dragicevic, Yeor Hafouta
We prove quenched and annealed statistical stability, linear response, and differentiability of asymptotic moments for parametric families of partially hyperbolic skew products, wi…
Robustness of nonuniform exponential dichotomies under a wider class of perturbations
Davor Dragicevic
The robustness property of exponential dichotomies refers to the stability of this notion under small linear perturbations. In recent work~\cite{PPX}, the authors have identified a…
h-Dichotomies via noncritical uniformity and expansiveness for evolution families
Davor Dragicevic
In a recent paper (Math. Ann. 393 (2025), 1769--1795), Elorreaga et al. have obtained a complete characterization of the notion of a -dichotomy for ordinary differential equatio…
Decay of correlations and limit theorems for random intermittent maps
Davor Dragicevic, Yeor Hafouta, Juho Leppanen
In this paper, we revisit the problem of polynomial memory loss and the central limit theorem for time-dependent LSV maps. More precisely, we show that for random LSV maps correspo…
Dichotomies for triangular systems on Hilbert spaces
Davor Dragicevic, Kenneth J. Palmer, Boris Petkovic
In this article, we study the relationship between the exponential dichotomy properties of a triangular system of linear difference equations and its associated diagonal system on…
Livšic regularity for random and sequential dynamics through transfer operators
Lucas Backes, Davor Dragicevic, Yeor Hafouta
We prove Livšic-type regularity results of coboundary representations for non-autonomous dynamical systems. Our results have an abstract nature and apply to several important speci…
Regularity of the variance in quenched CLT for random intermittent dynamical systems
Davor Dragičević, Juho Leppänen
We study random dynamical systems composed of LSV maps with varying parameters, without any mixing assumptions on the base space of random dynamics. We establish a quenched central…
Generalized dichotomies via time rescaling
Davor Dragicevic, Cesar M. Silva
For discrete-time nonautonomous linear dynamics and a large class of discrete growth rates , we show that the notion of dichotomy (with respect to a sequence of norms) can b…
Admissibility and generalized nonuniform dichotomies for nonautonomous Random Dynamical Systems
Davor Dragicevic, Cesar M. Silva, Helder Vilarinho
In this paper, we introduce generalized dichotomies for nonautonomous random linear dynamical systems acting on arbitrary Banach spaces, and obtain their complete characterization…
Linear response for random and sequential intermittent maps
Davor Dragicevic, Cecilia Gonzalez-Tokman, Julien Sedro
This work establishes a quenched (trajectory-wise) linear response formula for random intermittent dynamical systems, consisting of Liverani-Saussol-Vaienti maps with varying param…
Characterizing nonuniform hyperbolicity by Mather-type admissibility
Robin Chemnitz, Davor Davor Dragičević
We consider linear cocycles acting on Banach spaces which satisfy the assumptions of the multiplicative ergodic theorem. A cocycle is nonuniformly hyperbolic if all Lyapunov expone…
Hyers-Ulam stability
Davor Dragicevic, Masakazu Onitsuka
We introduce a new concept of Hyers-Ulam stability, in which in the size of a pseudosolution of a given ordinary differential equation and its deviation from an exact solution are…
A characterization of -dichotomies via admissibility
Lucas Backes, Davor Dragicevic
We present a characterization of -dichotomies in terms of the admissibility of certain pairs of weighted spaces for nonautonomous discrete time dynamics acting on Banach spa…
Effective quenched linear response for random dynamical systems
Davor Dragicevic, Yeor Hafouta
We prove ``effective'' linear response for certain classes of non-uniformly expanding random dynamical systems which are not necessarily composed in an i.i.d manner. In application…
Shadowing, Hyers--Ulam stability and hyperbolicity for nonautonomous linear delay differential equations
Lucas Backes, Davor Dragicevic, Mihaly Pituk
It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is av…
Hyers-Ulam stability for finite-dimensional nonautonomous dynamics
Davor Dragičević
The main purpose of this paper is to obtain necessary and sufficient conditions under which a nonautonomous, finite-dimensional and two-sided dynamics generated by a sequence of ma…
Shadowing and hyperbolicity for linear delay difference equations
Lucas Backes, Davor Dragicevic, Mihaly Pituk
It is known that hyperbolic linear delay difference equations are shadowable on the half-line. In this paper, we prove the converse and hence the equivalence between hyperbolicity…
Iterated invariance principle for random dynamical systems
Davor Dragicevic, Yeor Hafouta
We prove a weak iterated invariance principle for a large class of non-uniformly expanding random dynamical systems. In addition, we give a quenched homogenization result for fast-…
Takens Theorem for nonautonomous partially hyperbolic dynamical systems
Davor Dragičević, Xiao Tang, Wenmeng Zhang
Takens Theorem for a partially hyperbolic dynamics provides a normal linearization along the center manifold. In this paper, we give the nonautonomous version of Takens Theorem und…
Parameterized shadowing for nonautonomous dynamics
Lucas Backes, Davor Dragičević, Xiao Tang
For nonautonomous and nonlinear differential and difference equations depending on a parameter, we formulate sufficient conditions under which they exhibit , shadowi…
Conditional Lipschitz shadowing for ordinary differential equations
Lucas Backes, Davor Dragicevic, Masakazu Onitsuka +1
We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish t…