A note on the omega-chaos
This paper establishes sufficient conditions for the infinite direct product of a continuous self-map on a compact metric space to be -chaotic and applies these findings to construct examples of unusual -chaotic maps.
🔢 Category
math.DS
165 papers
Impacts of the duration and intensity of grazing cycle on vegetation population dynamics in semi-arid ecosystems with seasonal succession
This paper proposes a novel seasonal vegetation model to demonstrate that the duration and intensity of grazing cycles critically determine both the persistence of single populations and the competitive outcomes between species in semi-arid ecosystems.
Infinite linear patterns in sets of positive density
This paper characterizes all possible infinite linear configurations that exist within the shift of any set of positive upper Banach density, thereby unifying and generalizing Szemerédi's theorem on arithmetic progressions and the recent density finite sums theorem.
Continuity of asymptotic entropy on wreath products
This paper establishes the continuity of asymptotic entropy for random walks on wreath products (where is any countable group and is a hyper-FC-central group with a cubic-growth subgroup) by proving the continuity of non-return probabilities and demonstrating that weak continuity of harmonic measures implies entropy continuity, thereby extending known results to new classes of groups including linear and groups.
Constructing -free Hardy fields
The paper demonstrates that every Hardy field can be extended to an -free Hardy field, a result that connects to classical oscillation criteria and is used to resolve questions posed by Boshernitzan and generalize one of his theorems.
The Poisson boundary of wreath products
This paper provides a complete description of the Poisson boundary for wreath products under conditions where lamp configurations stabilize and the projected measure on is Liouville, thereby resolving a long-standing open question regarding the boundary for () with finite first moment measures.
A universal method to approach the Poincaré center problem
This paper establishes a universal method for solving the Poincaré center problem by proving that every analytic center admits a Laurent inverse integrating factor, thereby enabling a theoretical procedure to characterize centers in polynomial vector fields, including nontrivial families that have resisted previous approaches.
The extended future cover of a sofic shift
This paper introduces and analyzes a canonical cover of the future cover for sofic shifts, which either coincides with the original future cover or constitutes a genuine extension depending on the specific case.
Lorentzian Polynomials, Semipositive Cones, and Cone-Stable EVI Systems
This paper extends the theory of Lorentzian and completely log-concave polynomials to proper convex cones by defining -Lorentzian forms and associated semipositive cones, establishing their geometric properties and negative-dependence interpretations, and applying these results to derive new Lyapunov stability criteria for cone-constrained evolution variational inequality systems.
Rigidity of the dynamics of on representations into a compact group
This paper establishes that for a compact Lie group and sufficiently large rank , the dynamics of the automorphism group acting on the representation space exhibit algebraic rigidity, where orbit closures and invariant probability measures are algebraic in nature, analogous to Ratner's theorems.
Multiplier rigidity for complex Hénon maps
This paper establishes that complex Hénon maps of a fixed degree are determined up to finitely many choices by their multiplier spectra, extending McMullen's classical rigidity theorem to higher dimensions by proving the nonexistence of stable algebraic families through precise asymptotic bounds on Lyapunov exponents.
Spectral rigidity among ellipses, Bialy's conjecture and local extrema of Mather's beta function
This paper proves Bialy's conjecture by demonstrating that two ellipses are identical if their Mather beta functions coincide at one or two nonzero rotation numbers (with the latter condition requiring equal perimeters for a single rotation number), and discusses the implications of this result for local extremizers of the beta function.
The completion of the set of Lagrangians and applications to dynamics -- Based on lectures by C. Viterbo
This paper, based on C. Viterbo's 2025 CIME lectures, establishes fundamental properties of the completion of Lagrangian submanifolds under the spectral metric via the refined concept of -support and applies these results to conformally symplectic dynamics to generalize the notion of Birkhoff attractors.
On non-chaotic hyperbolic sets
This paper establishes the necessary and sufficient conditions that determine whether a hyperbolic set is chaotic or non-chaotic.
Localized state for nonlinear disordered stark model
This paper employs diagonalization of linear operators and KAM theory to prove the existence of time quasi-periodic, spatially localized states with arbitrary power-law decay in a nonlinear disordered Stark model for most random realizations and reasonable parameter ranges.
Uniform-in-diffusivity mixing by shear flows: stochastic and dynamical perspectives
This paper presents two novel, short proofs for the sharp uniform-in-diffusivity mixing rate of passive scalars in parallel shear flows with weak molecular diffusion, utilizing stochastic integration-by-parts to establish optimality under minimal regularity and a dynamical systems approach to provide a new perspective on shear-induced mixing.
On the height boundedness of periodic and preperiodic points of dominant rational self-maps on projective varieties
This paper refutes the conjecture that isolated periodic points of automorphisms on affine spaces have bounded height by providing a counterexample, while simultaneously proving that cohomologically hyperbolic dominant rational self-maps on projective varieties possess a Zariski open subset with height-bounded periodic points and offering evidence that such boundedness may fail for preperiodic points.
The Batchelor spectrum for a deterministically driven passive scalar
This paper establishes the first example of Batchelor's law for a passive scalar under deterministic forcing by proving that sufficiently smooth initial data in a specific time-periodic, Lipschitz velocity field converges to a limiting solution satisfying a cumulative form of the law.
Amplitude Dependent Bode Diagrams via Scaled Relative Graphs
This paper introduces a method for computing less conservative -gain bounds for nonlinear Lur'e systems over restricted frequency and amplitude ranges by combining Scaled Relative Graphs with Sobolev theory, resulting in a three-dimensional nonlinear generalization of the Bode diagram that recovers both the standard LTI Bode plot and the global -gain as limiting cases.
A Dynamical Approach to Non-Extensive Thermodynamics
This paper develops a non-extensive thermodynamic formalism for one-sided shifts by introducing -entropy and -pressure concepts, proving the existence and uniqueness of -equilibrium states for Lipschitz potentials, and establishing connections between these generalized structures and classical Ruelle transfer operators.