Related papers: On the tree models of mildly dissipative maps
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
Let M be a rank 1 affine invariant orbifold in a stratum of the moduli space of flat surfaces. We show that the leaves of the M-isoperiodic foliation are either all closed or all dense. In the second case, we establish ergodicity of the…
We study the dissipative dynamics of a class of interacting ``gamma-matrix'' spin models coupled to a Markovian environment. For spins on an arbitrary graph, we construct a Lindbladian that maps to a non-Hermitian model of free Majorana…
In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will…
We study shadowing-type properties for set-valued dynamical systems. In particular, we investigate the periodic shadowing property and its relationship with expansivity and chain transitivity. We establish that for positively expansive…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
A number of techniques have been developed to perturb the dynamics of $C^1$-diffeomorphisms and to modify the properties of their periodic orbits. For instance, one can locally linearize the dynamics, change the tangent dynamics, or create…
This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of…
When the Poincar\'{e} map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…
We prove a number of identities relating the sofic entropy of a certain class of non-expansive algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree entropy of Cayley graphs of residually finite groups. We…
We present new examples of open sets of diffeomorphisms such that a generic diffeomorphisms in those sets have no dynamically indecomposable attractors in the topological sense and have infinitely many chain-recurrence classes. We show that…
We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
Data streams are ubiquitous in modern business and society. In practice, data streams may evolve over time and cannot be stored indefinitely. Effective and transparent machine learning on data streams is thus often challenging. Hoeffding…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient…
Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…