70 citations · 273 across the 38 of their papers we have counts for
44 papers
A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem for connected Lie group actions
Yonatan Gutman, Qiang Huo, Kangbo Ouyang
Let be a connected Lie group equipped with a compatible right-invariant metric and let act continuously on a compact metrizable space . We prove that admits a -eq…
Generic Sharp Shift Embedding for Amenable Group Actions with the Uniform Rokhlin Property and Comparison
Yonatan Gutman, Chunlin Liu
Naryshkin recently proved that a free action of a countably infinite discrete amenable group on a compact metrizable space with the uniform Rokhlin property and comparison…
Dynamical Cantor Staircase Functions and The Small Flow Boundary Property
Tomasz Downarowicz, Yonatan Gutman, Chunlin Liu
The small flow boundary property (SFBP), introduced by Burguet for fixed-point free topological flows, is a non-trivial generalization of the small boundary property (SBP). We char…
A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem
Yonatan Gutman, Qiang Huo, Masaki Tsukamoto
We prove that a continuous action of on a compact metrizable space equivariantly embeds into the shift action on the space of one-Lipschitz functions from $\mathbb{R…
Optimal compressed sensing for mixing stochastic processes
Yonatan Gutman, Adam Śpiewak
Jalali and Poor introduced an asymptotic framework for compressed sensing of stochastic processes, demonstrating that any rate strictly greater than the mean information dimension…
On the representation of measurable and continuous dynamical systems by Lipschitz functions
Yonatan Gutman, Qiang Huo
Two representations theorems are presented: 1. Any Borel action of a second countable locally compact group on a standard Borel space admits an injective -equivariant Bo…
Predicting dynamical systems with too few time-delay measurements: error estimates
Krzysztof Barański, Yonatan Gutman, Adam Śpiewak
We study the problem of reconstructing and predicting the future of a dynamical system by the use of time-delay measurements of typical observables. Considering the case of too few…
Local mean dimension theory for sofic group actions
Felipe García-Ramos, Yonatan Gutman
Using a local perspective, we introduce \textit{mean dimension pairs} and give sufficient conditions of when every non-trivial factor of a continuous group action of a sofic group…
Equivariant embedding of finite-dimensional dynamical systems
Yonatan Gutman, Michael Levin, Tom Meyerovitch
We prove an equivariant version of the classical Menger-Nobeling theorem regarding topological embeddings: Whenever a group acts on a finite-dimensional compact metric space $X…
Regularity of almost-surely injective projections in Euclidean spaces
Krzysztof Barański, Yonatan Gutman, Adam Śpiewak
In a previous work we proved that if a finite Borel measure in a Euclidean space has Hausdorff dimension smaller than a positive integer , then the orthogonal projection ont…
Prediction of dynamical systems from time-delayed measurements with self-intersections
Krzysztof Barański, Yonatan Gutman, Adam Śpiewak
In the context of predicting the behaviour of chaotic systems, Schroer, Sauer, Ott and Yorke conjectured in 1998 that if a dynamical system defined by a smooth diffeomorphism o…
Strongly isomorphic symbolic extensions for expansive topological flows
Yonatan Gutman, Ruxi Shi
In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This…
On the Shroer-Sauer-Ott-Yorke predictability conjecture for time-delay embeddings
Krzysztof Barański, Yonatan Gutman, Adam Śpiewak
Shroer, Sauer, Ott and Yorke conjectured in 1998 that the Takens delay embedding theorem can be improved in a probabilistic context. More precisely, their conjecture states that if…
Maximal pronilfactors and a topological Wiener-Wintner theorem
Yonatan Gutman, Zhengxing Lian
For strictly ergodic systems, we introduce the class of CF-Nil() systems: systems for which the maximal measurable and maximal topological -step pronilfactors coincide as mea…
Around the variational principle for metric mean dimension
Yonatan Gutman, Adam Śpiewak
We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic…
On the structure theory of cubespace fibrations
Yonatan Gutman, Bingbing Liang
We study fibrations in the category of cubespaces/nilspaces. We show that a fibration of finite degree between compact ergodic gluing cubespaces (in parti…
Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable
Yonatan Gutman, Todor Tsankov, Andy Zucker
Answering a question of Uspenskij, we prove that if is a closed manifold of dimension or higher or the Hilbert cube, then the universal minimal flow of …
Strictly ergodic distal models and a new approach to the Host-Kra factors
Yonatan Gutman, Zhengxing Lian
Cocycles are a key object in Antolín Camarena and Szegedy's (topological) theory of nilspaces. We introduce measurable counterparts, named nilcycles, enabling us to give conditions…
New Uniform Bounds for Almost Lossless Analog Compression
Yonatan Gutman, Adam Śpiewak
Wu and Verdú developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal…
Metric mean dimension and analog compression
Yonatan Gutman, Adam Śpiewak
Wu and Verdú developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal…
A probabilistic Takens theorem
Krzysztof Barański, Yonatan Gutman, Adam Śpiewak
Let be a Borel set, a Borel probability measure on and a Lipschitz and injective map. Fix greater than the (Hausdorf…
A Lipschitz refinement of the Bebutov--Kakutani dynamical embedding theorem
Yonatan Gutman, Lei Jin, Masaki Tsukamoto
We prove that an -action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions if its fixed point set can be topol…
Mean dimension and an embedding theorem for real flows
Yonatan Gutman, Lei Jin
We develop mean dimension theory for -flows. We obtain fundamental properties and examples and prove an embedding theorem: Any real flow of mean dimens…
Application of signal analysis to the embedding problem of -actions
Yonatan Gutman, Yixiao Qiao, Masaki Tsukamoto
We study the problem of embedding arbitrary -actions into the shift action on the infinite dimensional cube . We prove that if a…