172 papers
This paper establishes that a hyperbolic polynomial with a connected Julia set is combinatorially rigid if and only if it is not of the "disjoint type," specifically proving that polynomials with attracting cycles attracting at least two critical points lack combinatorial rigidity.
This paper characterizes the real laminations of cubic polynomials on the tame boundaries of hyperbolic components of types (A), (B), and (C) by proving they are generated by the component's lamination and a single characteristic equivalence class, thereby demonstrating that all such hyperbolic cubic polynomials lack combinatorial rigidity.
This paper introduces loop braid groups as a three-dimensional generalization of classical braid groups to study homeomorphisms of the 3-ball, establishing a connection between Burau matrix representations and the generalized Lefschetz number to derive estimates for the existence and interaction of fixed and periodic points.
This paper classifies quadratic rational maps over with nonabelian automorphism groups that possess rational periodic points of periods 1, 2, and 3, proves the nonexistence of such points for periods 4 and 5, and establishes that the total number of rational preperiodic points is at most 6.
This paper presents a systematic method to construct vector fields that realize hierarchical excitable networks, where lower-level dynamics form heteroclinic connection patterns and top-level transitions between these patterns are excitable with zero threshold, thereby extending the simplex realization method of Ashwin and Postlethwaite.
The paper proves that transitive Anosov flows are abundant on fibered hyperbolic 3-manifolds by demonstrating that a finite index subgroup of the mapping class group consists of elements whose mapping tori carry such flows, thereby establishing that these manifolds have positive density within the set of all fibered hyperbolic 3-manifolds.
This paper generalizes the Newton-Puiseux Theorem to the context of planar real analytic vector fields by proving that every characteristic orbit of an isolated singularity admits a "power-log" asymptotic expansion.
This paper constructs Green currents associated with the dominant eigenspaces of holomorphic correspondences on compact Kähler manifolds under specific dynamical degree conditions, establishes the log-Hölder continuity of their super-potentials, and proves the exponential equidistribution of positive closed currents toward the main Green current when the correspondence exhibits simple cohomological action and satisfies a local multiplicity assumption.
This paper defines the topological pressure of continuous functions for holomorphic correspondences on the Riemann sphere using open covers and proves that this definition is equivalent to the existing approach based on separated and spanning families of orbits.
This paper constructs analytic symplectomorphisms on the sphere, disk, and cylinder that exhibit minimal ergodicity with exactly three ergodic measures by generalizing a principle introduced by Berger based on the Anosov-Katok approximation by conjugacy method.
This paper establishes the existence and uniqueness of a non-negative, piecewise smooth, and symmetric potential in that maximizes the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators, demonstrating that its nonzero part is determined by the solution to the pendulum equation via measure differential equations and weak convergence.
This paper establishes a sharp topological dichotomy for slices of the Sierpinski tetrahedron, demonstrating that slices at dyadic rational heights possess finitely many connected components with infinite first Čech homology, whereas slices at non-dyadic rational heights are totally disconnected with vanishing positive-degree homology.
This paper advances the study of outer length billiards by proving 3- and 4-periodic versions of the Ivrii conjecture and demonstrating the existence of functional spaces of billiard tables with invariant curves of -periodic points, including an explicit geometric parameterization for the centrally symmetric case.
This paper demonstrates that while topological classification of a specific "tears of the heart" polycycle unfolding suggests four invariants, a metrical perspective reveals that for Lebesgue almost all parameter values, only two such invariants exist.
Using an intermediate-complexity climate model, this study reveals that the Atlantic Meridional Overturning Circulation (AMOC) undergoes a boundary crisis under rising CO levels, where the collapse of its stable state and the resulting long chaotic transients governed by edge states explain large ensemble variances and apparent stochastic bifurcations in Earth system models.
This paper introduces a novel early warning signal called DE-AC, which estimates the dominant eigenvalue from autocorrelation functions to reliably predict the onset of period-doubling bifurcations in cardiac systems with superior sensitivity and specificity compared to existing indicators.
This paper introduces the Random Quadratic Form (RQF), a stochastic differential equation on a sphere that demonstrates how common noise induces synchronization and token clustering in deep transformers, offering an alternative explanation to self-attention for these phenomena.
This paper proposes a dynamical theory of adaptive coordination in multi-agent systems, demonstrating that intelligent behavior emerges from the structural coupling of agents, incentives, and a persistent environment through feedback loops, rather than from centralized optimization or rational expectations.
This paper establishes a cut and project scheme based on cocompact Fuchsian groups acting on the Poincaré disc, demonstrating that specific fundamental domains generate chaotic Delone sets with countably infinite tile lengths, thereby addressing the potential for improved graded metamaterials and extending previous work on hyperbolic aperiodic structures.
This paper demonstrates that spontaneous flow reversals in 2D active nematic turbulence are organized by a low-dimensional, symmetry-governed network of exact coherent structures and their invariant manifolds, which persist from the preturbulent regime into chaos to dictate the dynamics of flow switching.