Knowledge-guided search finds biological ODEs that data-fitting misses
MEDA shows literature-derived constraints, not trajectory fit, are the load-bearing part of recovering mechanistic models.
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Dynamical Systems
Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
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The paper proves existence of a C^r diffeomorphism on a closed manifold of dimension >2…
It stays strongly pluripotent only on the majority subset, creating a robust obstruction inside the affine family.
· “A robust obstruction to full strong pluripotency for wild blender-horseshoes”
Finite entropy systems cut subset entropy to any level
New proof answers an open question; infinite-measure entropy creates a zero-or-infinity gap
· “Hereditary Lowerability of Topological Dynamical Systems”
Geodesic flows gain integer periods via metric dictionary
Every continuous reparameterization is matched to a group metric; word metrics yield flows with all orbits of integer length.
· “A geometric correspondence for reparameterizations of geodesic flows”
Weak-form networks recover physical laws from noisy measurements
WGFINNs preserve exact thermodynamic constraints and deliver more accurate predictions than strong-form alternatives at all noise levels.
· “WGFINNs: Weak formulation-based GENERIC formalism informed neural networks”
Two numbers determine similarity-pair boundary dynamics
λ and θ encode the boundary map; if a conjecture holds, cut points are read from walks in a graph.
Tame groups are exactly the precompact ones
Short proof: any non-precompact group has a uniformly continuous function whose orbit is an ℓ1 basis.
All invariant C*-subalgebras of PSL_n(Z) arise from normal subgroups
For n≥3, PSL_n(Z)'s reduced C*-algebra has no exotic invariant subalgebras — rigidity matches the von Neumann case.
Generic 3D Klein sails get a Gauss-Kuzmin law
A flow cross-section with finite measure makes face statistics universal for almost every sail.
· “Generalised Gauss--Kuzmin Distribution for Klein sails in mathbb R³”
Central configurations reduce to a single rank-one matrix identity
A single rank-one factorization unifies the classical five-body and Dziobek systems, even on degenerate strata.
Period 2 forced for every graph in the middle chip band
Chip totals in the open band (2|E|-|V|, 2|E|) force every vertex to fire on alternate rounds.
· “All parallel chip-firing games with 2|E|-|V|<|σ|<2|E| have period 2”
ASL(Z)-invariant subsets come from polynomials and independent sampling
This higher-order cut-and-project yields Bernoulli mixtures under weak mixing and details Howe-Moore failure for the groups.
· “{ASL_n}(mathbb Z) invariant random subsets of mathbb Z^n”
Affine invariance threshold in prime fields is o(log p)
Density-1/2 sets satisfy |A Δ (ax+b)| = o(p) for all |a|,|b| = o(log p), solving Green's open problem 90.
· “Almost Affine Invariance Over Prime Fields: Green Problem 90”
Finitely generated G outside C ties amenability to Thompson F
The group is amenable exactly when F is, yet its minimal line actions lack a Borel transversal for conjugacy.
Invasion-wave speed falls strictly as diffusion ratio rises
A long-observed numerical monotonicity in the Lotka-Volterra strong-competition model now has an analytic proof
Weierstrass hoppings give quantum crystals arbitrarily fast dispersion
Lacunary hopping weights make wave packets flatten like |t|^{-N} for every N, with no universal speed limit.
· “Arbitrarily Fast Quantum Dispersion in Long-Range Crystals”
Explicit bound tames variation of multiple ergodic averages
Quantitative strengthening of the norm-convergence theorem with computable constants, verified in Lean 4.
A new example shows that a standard shadowing property used for flows does not always…
A suspension flow over the full shift with a continuous non-Hölder roof function has the shadowing property but fails local product…
· “Local Product Structure of Expansive Flows with Shadowing Property”
Global zeta fails
Even with infinitely many cusps, first-return data and a renormalized product keep orbit information computable.
· “Zeta renormalization and pressure at infinity for an infinitely cusped tree lattice”
Coupled-map large-N fluctuations are Gaussian
Chaos propagates and the CLT holds with explicit covariance and a 1/√N error rate.
· “Propagation of Chaos and Gaussian Fluctuations for Mean-field Coupled Maps”
Equilibrium measure fixes a generic polynomial map
For most regular endomorphisms of C^k, equal measures force equal maps—up to iteration in C^2.
· “Measure rigidity for regular polynomial endomorphisms and applications”
Inertial manifolds stabilize long-range PDE learning
A neural operator that splits solutions into a manifold coordinate and a residual beats FNO over long rollouts.
· “Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equations”
Periodic orbits reproduce Lyapunov exponents without Hölder regularity
Invariant holonomies replace the smoothness assumption and the result reaches discontinuous cocycles too.
· “Periodic approximation of Lyapunov exponents for cocycles admitting invariant holonomies”
Inertia makes high-dimensional sync transitions jump abruptly
Kuramoto model with inertia shows hysteresis beyond a dimension-dependent threshold; odd dimensions still jump at zero inertia.
· “Inertial synchronization of networked oscillators in arbitrary dimensions”
Orbit equivalence made explicit for rank-one actions
From cutting-and-stacking data alone, the paper builds orbit maps and a full topological invariant.
· “Explicit construction of orbit equivalence for rank-one actions”
Fixed shifts give Weibull and Fréchet laws for toral minima
Lacunary sampling of nearest-neighbour distances yields explicit Weibull, Fréchet, and logarithm laws.
· “Extreme values and logarithm laws for toral translations”
One derivation generates all four flight-control inversion laws
A unified equation yields model-based, sensory, incremental, and hybrid NDI laws and shows how to choose between them.
· “Dynamic Inversion: An Incrementally Evolving Methodology for Flight Control Design”
Logarithmic displacement law aligns velocities on curved manifolds
On hyperbolic space the alignment theorem holds unconditionally, without extra assumptions on trajectories.
This paper shows that a special kind of chaotic motion near a blender-horseshoe remains…
For every closed manifold of dimension at least three, there is an open set of C^1 diffeomorphisms whose wild blender-horseshoes are…
This paper builds a framework for deciding when a coarse
A framework using structured stochastic liftings, delay windows, and state-space enrichment to detect and repair non-closure in probability…
· “Identifying Probability Localization Dynamics via Structured Stochastic Liftings”
One flag set encodes every limit set of PSL(3,C) groups
The Myrberg set equals the union of limiting lines; four lines in the Kulkarni set force hyperbolicity.
· “Asymptotic flag geometry of complex Kleinian groups in mathbb{P}²_mathbb{C}”
One trichotomy rules all ways of observing chaos
Absolute and distributional chaos divide generically across all observation schemes.
Very slow-growing Borel graphs are hyperfinite
A growth exponent near 0.1523 settles the hyperfiniteness question for amenable actions of that growth.
Block Anderson Lyapunov exponents pinned to O(1/W)
Quantitative bounds on Lyapunov exponents imply localization length at most C W^2 for the 1D block Anderson model.
· “Quantitative Furstenberg Theory for Large Random Matrices”
Minimal nilrotations have connected diagonal polynomial orbit closures
Connectedness forces polynomial recurrence in every prescribed residue class and settles a conjecture.
· “Connectedness of polynomial diagonal orbit closures for minimal nilrotations and applications”
Fixed points break shadowing
On Schwartz space, the symbol's fixed points and derivative growth decide whether its operator shadows or expands.
· “Linear dynamics of composition operators on Schwartz spaces”
Finite-step Lyapunov certificates give recursive-feasible distributed MPC
Each subsystem solves one local problem; stability follows from an M-step Lyapunov estimate and a checked prediction margin
· “Distributed model predictive control via finite-step control Lyapunov functions”
One trained layer model yields SH dispersion for any substrate
PINN learns the interface derivative once; elastic, piezoelectric and piezomagnetic half-spaces reuse it.
For simple parabolic maps, basin conjugacy is global conjugacy
The conformal shape of one parabolic basin pins down the whole rational map, and parabolic basins can be perturbed to attracting ones.
Media-response delay can flip a stable epidemic into cycles
A model with vaccination and waning immunity shows that crossing a critical delay triggers sustained oscillations that never die out.
· “Stability and Hopf Bifurcation of a Delayed SVIRS Epidemic Model with Media Coverage”
At zero Lyapunov gap, exponents change at most logarithmically
For Markov GL(2) cocycles, perturbing matrices or transition kernel shifts both exponents by a log modulus.
· “Log-H\"oder continuity at zero Lyapunov gap for finite state Markov GL(2)-cocycles”
Multi-step training recovers sparse equations from noisy time series
Chaotic systems: short trajectories diverge, but long-run statistics match the true attractor.
· “Symbolic Neural ODEs: Learning interpretable models from time-series data”
Non-accessible perturbations are conjugate to the linear map
Near an ergodic torus automorphism with two-dimensional center, a single conjugacy makes every commuting homeomorphism affine.
A p-adic Littlewood counterexample would bring continuum many
Any non-empty exceptional set has positive 1/log(1/r)-Hausdorff measure; over finite fields the measure is infinite.
Once symptoms outpace resilience
Two coupled equations reproduce chronic, delayed, recovery and resilient depression courses.
Same nullcline identity links Hopf location and criticality
A five-term trace-field formula gives the first Lyapunov coefficient in predator-prey systems.
Countable set in R^9 has unequal Hausdorff and box dimensions
Three contracting maps build a sub-self-similar set whose two fractal dimensions disagree.
· “Sub-self-similar sets with distinct Hausdorff and Box dimensions”
Vaccination plus treatment beats either alone in HBV model
A new four-compartment model shows the basic reproduction number decides whether hepatitis B dies out or persists, and joint optimal…
Entropy gap controls d-bar distance to max-entropy measure
Any measure with entropy ε below the maximum lies within C√ε of the max-entropy measure in d-bar.
· “Effective uniqueness of the measure of maximal entropy in Ornstein's bar{d}-metric”
Symmetry turns quadratic 3D systems into gradient flows
A 19-parameter family of equations is now proved to have only converging bounded orbits, with zero entropy on every compact invariant set.
Three complete fields generate every algebraic vector field
So any smooth diffeomorphism isotopic to the identity can be approximated by just three time-independent flows.
· “Integrable Generators of Algebraic Vector Fields for Real Connected Semi-simple Matrix Groups”
One series erases contracting fibers from any Hölder potential
Entropy, pressure, equilibrium states, and minimizing measures then transfer exactly from the base dynamics.
Explicit construction makes Haar measure the unique maximizer
On any ergodic compact abelian group, Haar measure can be singled out by an explicit continuous function.
At a 3:2 crossing, one bounded generator replaces a divergent coefficient
The finite-window logarithm of the one-cycle Koopman operator stays bounded at zero detuning and recovers the Kerr jump: Ξ=3.52 vs 3.54
· “Resonance crossings as entire functions of the Koopman operator”
One log-determinant potential unites statistics and subspace learning
The same convex function drives dually flat manifolds, double-bracket flows, and singular blow-ups in one framework.
Prevalent surfaces on fractal products lose η at the horizon
On self-similar fractals, almost every continuous surface has box dimension exactly η above its horizon.
· “On the horizon problem over the product of self-similar fractals”
Treeable subrelation forces quasi-periodic almost equality class
A finite-index treeing produces a quasi-periodic almost equality class, advancing the finite index treeability problem.
Free Burnside groups of large odd exponent have cost 1
The proof also forces vanishing first ℓ²-Betti number and anti-treeability.
The entropy spectrum of a hyperbolic surface is reverse well-ordered
Subsurface entropies accumulate exactly where the complement still has room for a curve, with a real gap below 1.
Wave law makes direct force feedback delay-safe in teleoperation
Under constant delay, the true contact force reaches the operator as both robot velocities decay to zero.
Multi-model forecasts beat individuals via chaotic error cancellation
Reservoir computing isolates why the multi-model mean beats its members: errors cancel along the unstable manifold of chaos.
· “Understanding the superiority of multi-model ensemble forecasts through reservoir computing”
Every finite coloring hides a monochromatic nice recurrence set
One cell of any finite partition must itself be a set of nice recurrence—a long-open Ramsey question.
Prompt-aware Koopman scoring improves black-box LLM safety checks
Adding prompt embeddings to residual scores lifts F1 most where violations hinge on prompt-response interaction.
· “Enforcing LLM Safety through DMD-based Classification of Prompt-Response Embedding Dynamics”
One identity makes a predator-prey model's cancellations exact
All pure high-order terms trace to one factor, so hunting deeper singularities becomes solving one polynomial.
· “An exact structural identity and its normal form consequences in a modified Leslie--Gower model”
n folds give n limit cycles
Adding one breakpoint at a time and using infinity as an outer boundary yields the conjectured lower-bound counts.
· “The number of limit cycles of piecewise linear Li\'enard systems”
Shadowing conjecture resolved: false in Banach spaces
The answer to the open problem depends on whether surjectivity implies right invertibility.
· “Resolving the generalized hyperbolicity conjecture for shadowing”
Open-curve hyperbolic flow solved exactly
All self-similar motions fall into four classes; any curve can evolve to any other.
Observer linearization is now a Hessian check
A structural test on one Hessian matrix replaces costly Lie-bracket checks and PDE solving for nonlinear observers.
Trapping region collapses to one unstable manifold near tangency
Closure of an unstable manifold is the whole maximal attractor in planar perturbations of unimodal maps.
· “Maximal attractors for perturbations of unimodal maps near a homoclinic tangency”
Good measure simplices are realized by minimal homeomorphisms
Clopen evaluations build a dimension group whose order interval is exactly the clopen sets.
· “Affine Evaluation Maps, Dimension Groups, and Fair measures”
Two prototypes explain all degenerate 2D zero-one networks
A row-pattern check on the stoichiometric matrix decides degeneracy; steady states are binomial.
· “Characterization of Minimal Degenerate Zero-One Reaction Networks”
STRP lifts from finite-index subgroups to overgroups
The generic Cantor-action property climbs finite-index inclusions; its Borel rank lies between the second and fourth arithmetical levels.
· “Finite-Index Lifting of Strong Topological Rokhlin Property and Descriptive Complexity”
Two commuting maps with bounded fibers give hyperfinite relations
New proof: any two commuting bounded-to-one Borel maps generate an equivalence relation that is hyperfinite.
· “Hyperfiniteness of bounded-to-one actions of commutative monoids”
Nonflat tori refute a 1994 flatness question
For every n≥3, new curved tori give each primitive hypersurface class an area-minimizing foliation; stable norms can't detect flatness.
· “Minimal foliations, codimension-one stable norms, and a question of Bangert”
Fiberwise entropy equals topological entropy in expanding IFS
A single average of transfer-operator eigenvalues determines both fiber and total entropy.
· “A Relative Variational Principle for Expanding Iterated Function Systems”
Quasi-irreducibility is the absence of equators
For random C1 maps, this equivalence yields continuity and expansion criteria for Lyapunov exponents.
Attractors persist for every damping exponent α
One stabilizability estimate yields compact attractors, uniform H²×H¹ bounds, and a well-behaved α→0 limit.
· “Attractors and Singular Limits for a Quintic Wave Equation with Nonlocal Kelvin--Voigt Damping”
Rank the data, and a kernel recovers drift and diffusion
Ordered diffusion kernels convert an ordering function into an SDE generator, decoupling drift from noise.
Graph splitting detects chaotic itinerancy without orbit-watching
A coarse grid, a Markov chain, and a filter expose ordered epochs inside chaotic dynamics—no trajectory inspection required.
· “Set-Oriented Approach to the Analysis of Chaotic Itinerancy”
Liénard systems get a sharper Hilbert-number lower bound
For every n≥2, cycles born near infinity and near a two-cuspidal lips polycycle coexist in one family.
· “Cyclicity of lips and center-focus problem near infinity”
