[
    {
        "id": "thesis:5731",
        "collection": "thesis",
        "collection_id": "5731",
        "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04212010-181932550",
        "primary_object_url": {
            "basename": "thesis.pdf",
            "content": "final",
            "filesize": 437456,
            "license": "other",
            "mime_type": "application/pdf",
            "url": "/5731/1/thesis.pdf",
            "version": "v4.0.0"
        },
        "type": "thesis",
        "title": "Dynamics of Non-Classical Interval Exchanges",
        "author": [
            {
                "family_name": "Gadre",
                "given_name": "Vaibhav S.",
                "orcid": "0000-0003-4222-9551",
                "clpid": "Gadre-Vaibhav-S"
            }
        ],
        "thesis_advisor": [
            {
                "family_name": "Calegari",
                "given_name": "Danny C.",
                "orcid": "0009-0007-9304-2822",
                "clpid": "Calegari-D"
            },
            {
                "family_name": "Dunfield",
                "given_name": "Nathan M.",
                "orcid": "0000-0002-9152-6598",
                "clpid": "Dunfield-N-M"
            }
        ],
        "thesis_committee": [
            {
                "family_name": "Calegari",
                "given_name": "Danny C.",
                "orcid": "0009-0007-9304-2822",
                "clpid": "Calegari-D"
            },
            {
                "family_name": "Dunfield",
                "given_name": "Nathan M.",
                "orcid": "0000-0002-9152-6598",
                "clpid": "Dunfield-N-M"
            },
            {
                "family_name": "Ramakrishnan",
                "given_name": "Dinakar",
                "orcid": "0000-0002-0159-087X",
                "clpid": "Ramakrishnan-D"
            },
            {
                "family_name": "Ni",
                "given_name": "Yi",
                "orcid": "0000-0002-5287-4258",
                "clpid": "Ni-Yi"
            }
        ],
        "local_group": [
            {
                "literal": "div_pma"
            }
        ],
        "abstract": "Train tracks with a single vertex are a generalization of interval exchange maps. Here, we consider non-classical interval exchanges: complete train tracks with a single vertex. These can be studied as a dynamical system by considering Rauzy induction in this context. This gives a refinement process on the parameter space similar to Kerckhoff's simplicial systems. We show that the refinement process gives an expansion that has a key dynamical property called uniform distortion. We use uniform distortion to prove normality of the expansion. Consequently, we prove an analog of Keane's conjecture: almost every non-classical interval exchange is uniquely ergodic. In the concluding chapter, we state an application of the main results of the thesis to a question about harmonic measures on the Thurston boundary of Teichmuller space coming from finitely supported random walks on the mapping class group.",
        "doi": "10.7907/082X-F229",
        "publication_date": "2010-06-11",
        "thesis_type": "phd",
        "thesis_year": "2010"
    }
]