169 papers
This paper utilizes the complexity function of invariant subsets in two-sided shift spaces to calculate the polynomial entropy of induced dynamics on hyperspaces of continua for specific one-dimensional systems and establishes a criterion for the induced map to possess infinite topological entropy.
This paper investigates the shadowing phenomenon for composition operators on the Hardy space , specifically characterizing those induced by linear fractional self-maps of the unit disk that possess the positive shadowing property.
This paper establishes the linear independence of complete elliptic integrals of the first, second, and third kinds to derive an upper bound on the zeros of their polynomial combinations, which is then applied to analyze the bifurcation of limit cycles in a Hamiltonian triangle system under small piecewise smooth perturbations.
This paper proposes and analyzes a dynamical model for group formation where new members probabilistically join groups based on size-inversely proportional attraction modulated by bias terms, deriving the conditions for stationary equilibrium and exploring the system's rich nonlinear behavior through both theoretical analysis and simulations.
This paper establishes a fundamental mathematical theory for second-order Filippov systems, demonstrating that crossing orbits spiral around invisible-invisible tangency surfaces to converge toward a well-defined second-order sliding motion governed by a derived vector field, without exhibiting finite-time Zeno behavior.
This paper establishes the area law for the entanglement entropy of free fermions in non-random ergodic fields by proving uniform eigenfunction localization and exponential decay of correlators for quasiperiodic, limit-periodic, and subshift-generated potentials, thereby extending previous results that were limited to random systems.
This paper investigates the non-autonomous dynamics of randomly iterated cubic polynomials of the form , establishing that totally disconnected Julia sets occur densely and almost surely under specific probabilistic conditions, even in the absence of hyperbolicity.
This paper establishes Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies by employing a novel dynamical rigidity argument.
This paper proposes a fully data-driven framework that combines adaptively computed, mechanism-aware precursors based on Optimal Time-Dependent (OTD) modes with a Transformer model to significantly extend the prediction horizons for extreme events in high-dimensional chaotic systems like Kolmogorov flow without requiring knowledge of the underlying governing equations.
This study investigates how inertial effects influence autotoxicity-mediated vegetation patterns on sloped arid terrains using a hyperbolic extension of the Klausmeier model, revealing that inertia acts as a destabilizing mechanism that enlarges the parameter range for uphill migrating bands, can induce hysteresis by reversing bifurcation regimes near onset, and increases pulse speeds in far-from-equilibrium conditions.
This paper proves that the homeomorphic speedup of a linearly recurrent two-sided subshift preserves the property of linear recurrence, thereby demonstrating that this strong form of minimality is invariant under such time changes.
This paper proves that for finite-dimensional quantum systems undergoing single-branch collapse dynamics without information erasure, operational irreversibility is structurally impossible because every physically admissible collapse selector contains a forward-invariant subset of states that can be connected with arbitrarily high precision and negligible energy cost, thereby establishing islands of quasi-reversibility.
This paper establishes the existence of traveling wave solutions, including non-monotone waves and front-pulse waves, for the two-species weak competition Lotka-Volterra system across all wave speeds , with a rigorous proof for the critical speed case and the first-time demonstration of front-pulse waves in the critical weak competition regime.
This paper introduces a canonical -algebra of operators with finite dynamical propagation for non-singular group actions, establishing its isomorphism to the algebraic crossed product under free actions to characterize ergodicity and to describe the Roe algebras of warped spaces and warped cones.
This paper introduces a novel frequency response formulation for nonlinear systems within the Koopman operator framework, deriving a generalized complex-valued function via Laplace transforms and resolvent theory to enable Bode plot analysis under specific existence conditions.
This study demonstrates that neglecting vaccine unwillingness in epidemiological models introduces significant errors in both long-term equilibrium predictions and short-term epidemic wave simulations, with the magnitude of error depending on the disease's infectivity and the speed of vaccination programs.
This paper establishes that for most parameter sets, the symmetry group of Markoff-type equations acts transitively on the majority of solutions modulo for a density one set of primes, with specific applications proving near-complete transitivity results for the -classification conjecture in and for solutions arising from generalized cluster algebras.
This paper introduces a notion of semistability for intrinsic reductions of non-archimedean rational functions at non-classical points in the Berkovich projective line and computes the resulting loci for quadratic rational iterations via a slope formula, demonstrating that these loci exhibit precise stationarity analogous to the polynomial case.
This paper establishes an explicit second-order expansion for the volume dimension of the Julia sets of holomorphic skew products in as a perturbation parameter approaches zero, extending the classical Ruelle-McMullen results on Hausdorff dimension to non-conformal higher-dimensional dynamical systems.
This paper establishes an asymptotic expansion in inverse powers of time for the correlation functions of isometric extensions of volume-preserving Anosov flows defined on Abelian covers of closed manifolds.