About this digest
Every weekday morning Claude, an AI model by Anthropic, reads the new arXiv papers in math.DS (Dynamical Systems) and math.GN (General Topology) and sorts them by how closely they match a research profile in topological dynamics and continuum theory.
The ranking follows that one profile, listed in full below. Anyone with overlapping interests is welcome to read along.
How papers are sorted
- High priority
- Central to the research profile below, or written by a followed author. Each gets a structured summary.
- Related / possibly interesting
- A real connection to the profile without being central. Also summarized.
- Low priority
- Everything else; listed by title only and collapsed by default.
- Top picks
- Up to three papers per day suggested as the first ones to read.
“High priority” means high priority for this profile, not a judgement of quality or importance.
Research profile
High priority, when one of these is central
- continuum theory (metric continua, Peano continua, dendrites, dendroids, arc-like, circle-like and tree-like continua)
- indecomposable and hereditarily indecomposable continua (pseudo-arc, pseudo-circle, Knaster continua, solenoids)
- inverse limits and inverse limit representations, including inverse limits of interval, tent, unimodal and graph maps
- the Ingram conjecture and classification of inverse limits of tent maps, including restrictions to the dynamical core
- dynamics on continua and other compacta, including homeomorphisms and maps of continua
- transitivity, mixing, weak mixing, exactness, locally eventually onto (LEO) maps, specification and shadowing
- generic and typical properties of maps or homeomorphisms in the Baire category sense
- one-dimensional dynamics (interval, circle, graph, tree and dendrite maps)
- topological dynamics on manifolds and almost manifolds where continuum-theoretic structure is central
- planar and surface homeomorphisms with continuum-theoretic content (attractors, rotation sets, prime ends, Birkhoff-type attractors)
- topological entropy and chaos notions (Li-Yorke, Devaney, distributional chaos) in topological dynamics
- Peano continua and mixing or exact self-maps of them
A math.GN paper about continua, inverse limits or one-dimensional spaces counts as high priority even without any dynamics.
Related / possibly interesting
- topological dynamics in general (minimality, proximality, equicontinuity, factors, flows on compact spaces)
- symbolic dynamics, subshifts, odometers and Toeplitz flows used as models for maps of continua
- group actions on continua, dendrites and one-dimensional spaces
- ergodic theory and invariant measures with a topological or one-dimensional component
- constructions of diffeomorphisms or homeomorphisms with prescribed properties (Anosov-Katok and approximation by conjugation)
- smooth, hyperbolic or complex dynamics where the topology of invariant sets (Julia sets, attractors, laminations) is central
- celestial mechanics and Hamiltonian dynamics, especially surveys or expository work
- general topology of hyperspaces, dimension theory and shape theory as they apply to continua
- surveys and expository papers on topological dynamics, ergodic theory or group actions
Usually low priority
- ODE-centered work with little connection to the topics above
- PDE-centered dynamical systems with little connection to the topics above
- numerical bifurcation analysis
- applied biological, physical, engineering, or control-oriented dynamics
- computation-heavy modeling unless a high-priority theme is central
- general topology unrelated to continua or dynamics (set-theoretic topology, cardinal invariants, topological algebra, function spaces, point-free topology)
Smooth, ODE or PDE methods alone never push a paper down when a high-priority theme is central; when in doubt between related and low, a paper is marked related.
High and related papers carry one to three topic tags from this list:
continuum theoryinverse limitsinterval and graph mapscircle and one-dimensional dynamicsplanar and surface dynamicsmixing and transitivityshadowing and specificationgenericityentropy and chaossymbolic dynamicsminimal systems and factorsgroup actionsergodic theorycomplex dynamicssmooth and hyperbolic dynamicsflows and foliationscelestial mechanicshyperspaces and descriptive topologyfractals and dimensionsurvey
How it is made
At 05:30 (Warsaw time) a GitHub Action saves the official arXiv RSS listing for math.DS and math.GN and extracts the text of the new papers. At about 07:00 Claude, an AI model by Anthropic, reads every title and abstract, classifies the papers and writes the summaries; the site is then rebuilt and published. Summaries are based on the title and abstract. For high-priority papers Claude also reads the introduction, and for the day's top picks a longer part of the paper; that reading appears in the “In the paper” section of the paper's card. Even so, summaries can miss or misstate details, and proofs are not checked. Always check the paper itself.
Replacement-only announcements and papers already reported on an earlier day are skipped. The reports for 5–8 October 2026 were rebuilt from archived math.DS listings and do not include math.GN.
Following along
- RSS / Atom feed of high-priority and related papers, for any feed reader.
- Weekly summaries collect each week's high and related papers on one page.
- Search covers every report.
- The ☆ star saves a paper to favorites in your own browser; favorites can be copied as a list or downloaded as BibTeX from the home page.
Credits
Adapted from daily-math-ds-digest by Xulei Wang, whose rendering, validation and archive design this site reuses. Formulas are rendered with MathJax ahead of time.